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class="vector-toc-numb">2</span> <span>Hall effect within voids</span> </div> </a> <button aria-controls="toc-Hall_effect_within_voids-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Hall effect within voids subsection</span> </button> <ul id="toc-Hall_effect_within_voids-sublist" class="vector-toc-list"> <li id="toc-Hall_effect_superposition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hall_effect_superposition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Hall effect superposition</span> </div> </a> <ul id="toc-Hall_effect_superposition-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Theory</span> </div> </a> <button aria-controls="toc-Theory-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Theory subsection</span> </button> <ul id="toc-Theory-sublist" class="vector-toc-list"> <li id="toc-Hall_effect_in_semiconductors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hall_effect_in_semiconductors"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Hall effect in semiconductors</span> </div> </a> <ul id="toc-Hall_effect_in_semiconductors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationship_with_star_formation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relationship_with_star_formation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Relationship with star formation</span> </div> </a> <ul id="toc-Relationship_with_star_formation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_Hall_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_Hall_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Quantum Hall effect</span> </div> </a> <ul id="toc-Quantum_Hall_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spin_Hall_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spin_Hall_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Spin Hall effect</span> </div> </a> <ul id="toc-Spin_Hall_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Quantum_spin_Hall_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Quantum_spin_Hall_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Quantum spin Hall effect</span> </div> </a> <ul id="toc-Quantum_spin_Hall_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Anomalous_Hall_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Anomalous_Hall_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Anomalous Hall effect</span> </div> </a> <ul id="toc-Anomalous_Hall_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hall_effect_in_ionized_gases" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hall_effect_in_ionized_gases"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Hall effect in ionized gases</span> </div> </a> <ul id="toc-Hall_effect_in_ionized_gases-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_Hall_effects" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_Hall_effects"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Other Hall effects</span> </div> </a> <ul id="toc-Other_Hall_effects-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Corbino_effect" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Corbino_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Corbino effect</span> </div> </a> <ul id="toc-Corbino_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hall effect</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" 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Available in 48 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-48" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">48 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A3%D8%AB%D9%8A%D8%B1_%D9%87%D9%88%D9%84" title="تأثير هول – Arabic" lang="ar" hreflang="ar" data-title="تأثير هول" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Holl_effekti" title="Holl effekti – Azerbaijani" lang="az" hreflang="az" data-title="Holl effekti" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%B2_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%AD%E0%A6%BE%E0%A6%AC" title="হল প্রভাব – Bangla" lang="bn" hreflang="bn" data-title="হল প্রভাব" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%A5%D0%BE%D0%BB%D0%B0" title="Эфект Хола – Belarusian" lang="be" hreflang="be" data-title="Эфект Хола" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%A5%D0%BE%D0%BB" title="Ефект на Хол – Bulgarian" lang="bg" hreflang="bg" data-title="Ефект на Хол" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Hall" title="Efecte Hall – Catalan" lang="ca" hreflang="ca" data-title="Efecte Hall" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hall%C5%AFv_jev" title="Hallův jev – Czech" lang="cs" hreflang="cs" data-title="Hallův jev" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hall-effekt" title="Hall-effekt – Danish" lang="da" hreflang="da" data-title="Hall-effekt" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hall-Effekt" title="Hall-Effekt – German" lang="de" hreflang="de" data-title="Hall-Effekt" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Halli_efekt" title="Halli efekt – Estonian" lang="et" hreflang="et" data-title="Halli efekt" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Hall" title="Efecto Hall – Spanish" lang="es" hreflang="es" data-title="Efecto Hall" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%AB%D8%B1_%D9%87%D8%A7%D9%84" title="اثر هال – Persian" lang="fa" hreflang="fa" data-title="اثر هال" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Effet_Hall" title="Effet Hall – French" lang="fr" hreflang="fr" data-title="Effet Hall" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Iarmhairt_Hall" title="Iarmhairt Hall – Irish" lang="ga" hreflang="ga" data-title="Iarmhairt Hall" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%99%80_%ED%9A%A8%EA%B3%BC" title="홀 효과 – Korean" lang="ko" hreflang="ko" data-title="홀 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%B8%D5%AC%D5%AB_%D5%A7%D6%86%D5%A5%D5%AF%D5%BF" title="Հոլի էֆեկտ – Armenian" lang="hy" hreflang="hy" data-title="Հոլի էֆեկտ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B9%E0%A4%BE%E0%A4%B2_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B5" title="हाल प्रभाव – Hindi" lang="hi" hreflang="hi" data-title="हाल प्रभाव" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Hallov_u%C4%8Dinak" title="Hallov učinak – Croatian" lang="hr" hreflang="hr" data-title="Hallov učinak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Efek_Hall" title="Efek Hall – Indonesian" lang="id" hreflang="id" data-title="Efek Hall" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Hall" title="Effetto Hall – Italian" lang="it" hreflang="it" data-title="Effetto Hall" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%A7%D7%98_%D7%94%D7%95%D7%9C" title="אפקט הול – Hebrew" lang="he" hreflang="he" data-title="אפקט הול" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%B0%E1%83%9D%E1%83%9A%E1%83%98%E1%83%A1_%E1%83%94%E1%83%A4%E1%83%94%E1%83%A5%E1%83%A2%E1%83%98" title="ჰოლის ეფექტი – Georgian" lang="ka" hreflang="ka" data-title="ჰოლის ეფექტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Holla_efekts" title="Holla efekts – Latvian" lang="lv" hreflang="lv" data-title="Holla efekts" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Holo_efektas" title="Holo efektas – Lithuanian" lang="lt" hreflang="lt" data-title="Holo efektas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hall-effektus" title="Hall-effektus – Hungarian" lang="hu" hreflang="hu" data-title="Hall-effektus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hall-effect" title="Hall-effect – Dutch" lang="nl" hreflang="nl" data-title="Hall-effect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9B%E3%83%BC%E3%83%AB%E5%8A%B9%E6%9E%9C" title="ホール効果 – Japanese" lang="ja" hreflang="ja" data-title="ホール効果" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hall-effekt" title="Hall-effekt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Hall-effekt" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Halleffekt" title="Halleffekt – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Halleffekt" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%B9%E0%AC%B2%E0%AD%8D_%E0%AC%AA%E0%AD%8D%E0%AC%B0%E0%AC%AD%E0%AC%BE%E0%AC%AC" title="ହଲ୍ ପ୍ରଭାବ – Odia" lang="or" hreflang="or" data-title="ହଲ୍ ପ୍ରଭାବ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Efet_Hall" title="Efet Hall – Piedmontese" lang="pms" hreflang="pms" data-title="Efet Hall" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Zjawisko_Halla" title="Zjawisko Halla – Polish" lang="pl" hreflang="pl" data-title="Zjawisko Halla" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Hall" title="Efeito Hall – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Hall" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Efectul_Hall" title="Efectul Hall – Romanian" lang="ro" hreflang="ro" data-title="Efectul Hall" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%A5%D0%BE%D0%BB%D0%BB%D0%B0" title="Эффект Холла – Russian" lang="ru" hreflang="ru" data-title="Эффект Холла" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Efekti_i_Hollit" title="Efekti i Hollit – Albanian" lang="sq" hreflang="sq" data-title="Efekti i Hollit" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hallov_jav" title="Hallov jav – Slovak" lang="sk" hreflang="sk" data-title="Hallov jav" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hallov_pojav" title="Hallov pojav – Slovenian" lang="sl" hreflang="sl" data-title="Hallov pojav" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%BE%D0%BB%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Холов ефекат – Serbian" lang="sr" hreflang="sr" data-title="Холов ефекат" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / 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lang="tr" hreflang="tr" data-title="Hall etkisi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%A5%D0%BE%D0%BB%D0%BB%D0%B0" title="Ефект Холла – Ukrainian" lang="uk" hreflang="uk" data-title="Ефект Холла" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hi%E1%BB%87u_%E1%BB%A9ng_Hall" title="Hiệu ứng Hall – Vietnamese" lang="vi" hreflang="vi" data-title="Hiệu ứng Hall" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Electromagnetic effect in physics</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the Colombian band, see <a href="/wiki/The_Hall_Effect_(band)" title="The Hall Effect (band)">The Hall Effect (band)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hall_effect.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Hall_effect.png/310px-Hall_effect.png" decoding="async" width="310" height="311" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Hall_effect.png/465px-Hall_effect.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Hall_effect.png/620px-Hall_effect.png 2x" data-file-width="984" data-file-height="986" /></a><figcaption>In diagram <b>A</b>, the flat conductor possesses a negative charge on the top (symbolized by the blue color) and a positive charge on the bottom (red color). In <b>B</b> and <b>C</b>, the direction of the electrical and the magnetic fields are changed respectively which switches the polarity of the charges around. In <b>D</b>, both fields change direction simultaneously which results in the same polarity as in diagram <b>A</b>. <div><ol><li>electrons</li><li>flat conductor, which serves as a hall element <i>(<a href="/wiki/Hall_effect_sensor" title="Hall effect sensor">hall effect sensor</a>)</i></li><li>magnet</li><li>magnetic field</li><li>power source</li></ol></div></figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist 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a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Electromagnetism" title="Electromagnetism">Electromagnetism</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File/Frameless"><a href="/wiki/File:VFPt_Solenoid_correct2.svg" class="mw-file-description" title="Solenoid"><img alt="Solenoid" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/190px-VFPt_Solenoid_correct2.svg.png" decoding="async" width="190" height="78" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/285px-VFPt_Solenoid_correct2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/VFPt_Solenoid_correct2.svg/380px-VFPt_Solenoid_correct2.svg.png 2x" data-file-width="490" data-file-height="200" /></a></span></td></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electricity" title="Electricity">Electricity</a></li> <li><a href="/wiki/Magnetism" title="Magnetism">Magnetism</a></li> <li><a href="/wiki/Optics" title="Optics">Optics</a></li> <li><a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational</a></li> <li><a href="/wiki/List_of_textbooks_in_electromagnetism" title="List of textbooks in electromagnetism">Textbooks</a></li> <li><a href="/wiki/List_of_electrical_phenomena" title="List of electrical phenomena">Phenomena</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a href="/wiki/Magnetic_scalar_potential" title="Magnetic scalar potential">Magnetic scalar potential</a></li> <li><a href="/wiki/Magnetic_vector_potential" title="Magnetic vector potential">Magnetic vector potential</a></li> <li><a href="/wiki/Magnetization" title="Magnetization">Magnetization</a></li> <li><a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">Permeability</a></li> <li><a href="/wiki/Right-hand_rule#Electromagnetism" title="Right-hand rule">Right-hand rule</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Electrodynamics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrical_network" title="Electrical network">Electrical network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Alternating_current" title="Alternating current">Alternating current</a></li> <li><a href="/wiki/Capacitance" title="Capacitance">Capacitance</a></li> <li><a href="/wiki/Current_density" title="Current density">Current density</a></li> <li><a href="/wiki/Direct_current" title="Direct current">Direct current</a></li> <li><a href="/wiki/Electric_current" title="Electric current">Electric current</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electrolysis" title="Electrolysis">Electrolysis</a></li> <li><a href="/wiki/Electromotive_force" title="Electromotive force">Electromotive force</a></li> <li><a href="/wiki/Electrical_impedance" title="Electrical impedance">Impedance</a></li> <li><a href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a href="/wiki/Resonator#Electromagnetics" title="Resonator">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>Hall effect</b> is the production of a <a href="/wiki/Voltage" title="Voltage">potential difference</a> (the <b>Hall voltage</b>) across an <a href="/wiki/Electrical_conductor" title="Electrical conductor">electrical conductor</a> that is <a href="https://en.wiktionary.org/wiki/transverse" class="extiw" title="wikt:transverse">transverse</a> to an <a href="/wiki/Electric_current" title="Electric current">electric current</a> in the conductor and to an applied <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> <a href="https://en.wiktionary.org/wiki/perpendicular" class="extiw" title="wikt:perpendicular">perpendicular</a> to the current. It was discovered by <a href="/wiki/Edwin_Hall" title="Edwin Hall">Edwin Hall</a> in 1879.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>The <i>Hall coefficient</i> is defined as the ratio of the induced <a href="/wiki/Electric_field" title="Electric field">electric field</a> to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the <a href="/wiki/Charge_carriers" class="mw-redirect" title="Charge carriers">charge carriers</a> that constitute the current. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Discovery">Discovery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=1" title="Edit section: Discovery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/History_of_electromagnetic_theory" title="History of electromagnetic theory">History of electromagnetic theory</a></div> <p>Wires carrying current in a magnetic field experience a <a href="/wiki/Mechanical_force" class="mw-redirect" title="Mechanical force">mechanical force</a> perpendicular to both the current and magnetic field. </p><p>In the 1820s, <a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">André-Marie Ampère</a> observed this underlying mechanism that led to the discovery of the Hall effect.<sup id="cite_ref-:1_3-0" class="reference"><a href="#cite_note-:1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> However it was not until a solid mathematical basis for <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> was systematized by <a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">James Clerk Maxwell</a>'s "<a href="/wiki/On_Physical_Lines_of_Force" title="On Physical Lines of Force">On Physical Lines of Force</a>" (published in 1861–1862) that details of the interaction between magnets and electric current could be understood. </p><p><a href="/wiki/Edwin_Hall" title="Edwin Hall">Edwin Hall</a> then explored the question of whether magnetic fields interacted with the conductors <i>or</i> the electric current, and reasoned that if the force was specifically acting on the current, it should crowd current to one side of the wire, producing a small measurable voltage.<sup id="cite_ref-:1_3-1" class="reference"><a href="#cite_note-:1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In 1879, he discovered this <i>Hall effect</i> while he was working on his doctoral degree at <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a> in <a href="/wiki/Baltimore" title="Baltimore">Baltimore</a>, <a href="/wiki/Maryland" title="Maryland">Maryland</a>.<sup id="cite_ref-bridgeman-momoir_4-0" class="reference"><a href="#cite_note-bridgeman-momoir-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Eighteen years before the <a href="/wiki/Electron" title="Electron">electron</a> was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental <a href="https://en.wiktionary.org/wiki/tour_de_force" class="extiw" title="wikt:tour de force">tour de force</a>, published under the name "On a New Action of the Magnet on Electric Currents".<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Hall_effect_within_voids">Hall effect within voids</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=2" title="Edit section: Hall effect within voids"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <b>ordinary Hall effect</b> can be used to distinguish the effect described in the introduction from a related effect which occurs across a void or hole in a <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> or metal plate when current is injected via contacts that lie on the boundary or edge of the void. The charge then flows outside the void, within the metal or semiconductor material. The effect becomes observable, in a perpendicular applied magnetic field, as a Hall voltage appearing on either side of a line connecting the current-contacts. It exhibits apparent sign reversal in comparison to the "ordinary" effect occurring in the simply connected specimen. It depends only on the current injected from within the void.<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hall_effect_superposition">Hall effect superposition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=3" title="Edit section: Hall effect superposition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Superposition of these two forms of the effect, the ordinary and void effects, can also be realized. First imagine the "ordinary" configuration, a simply connected (void-less) thin rectangular homogeneous element with current-contacts on the (external) boundary. This develops a Hall voltage, in a perpendicular magnetic field. Next, imagine placing a rectangular void within this ordinary configuration, with current-contacts, as mentioned above, on the interior boundary of the void. (For simplicity, imagine the contacts on the boundary of the void lined up with the ordinary-configuration contacts on the exterior boundary.) In such a combined configuration, the two Hall effects may be realized and observed simultaneously in the same doubly connected device: A Hall effect on the external boundary that is proportional to the current injected only via the outer boundary, and an apparently sign-reversed Hall effect on the interior boundary that is proportional to the current injected only via the interior boundary. The superposition of multiple Hall effects may be realized by placing multiple voids within the Hall element, with current and voltage contacts on the boundary of each void.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Further "Hall effects" may have additional physical mechanisms but are built on these basics. </p> <div class="mw-heading mw-heading2"><h2 id="Theory">Theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=4" title="Edit section: Theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Hall effect is due to the nature of the current in a conductor. Current consists of the movement of many small <a href="/wiki/Charge_carrier" title="Charge carrier">charge carriers</a>, typically <a href="/wiki/Electron" title="Electron">electrons</a>, <a href="/wiki/Electron_hole" title="Electron hole">holes</a>, <a href="/wiki/Ion" title="Ion">ions</a> (see <a href="/wiki/Electromigration" title="Electromigration">Electromigration</a>) or all three. When a magnetic field is present, these charges experience a force, called the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> When such a magnetic field is absent, the charges follow approximately straight paths between collisions with impurities, <a href="/wiki/Phonons" class="mw-redirect" title="Phonons">phonons</a>, etc. However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved; thus, moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge density across the Hall element, arising from a force that is perpendicular to both the straight path and the applied magnetic field. The separation of charge establishes an <a href="/wiki/Electric_field" title="Electric field">electric field</a> that opposes the migration of further charge, so a steady <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> is established for as long as the charge is flowing.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">classical electromagnetism</a> electrons move in the opposite direction of the current <span class="texhtml"><i>I</i></span> (by <a href="/wiki/Electric_current#Conventions" title="Electric current">convention</a> "current" describes a theoretical "hole flow"). In some metals and semiconductors it <i>appears</i> "holes" are actually flowing because the direction of the voltage is opposite to the derivation below. </p> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:Hall_Effect_Measurement_Setup_for_Electrons.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/1/19/Hall_Effect_Measurement_Setup_for_Electrons.png" decoding="async" width="285" height="184" class="mw-file-element" data-file-width="285" data-file-height="184" /></a><figcaption>Hall effect measurement setup for electrons. Initially, the electrons follow the curved arrow, due to the magnetic force. At some distance from the current-introducing contacts, electrons pile up on the left side and deplete from the right side, which creates an electric field <span class="texhtml"><i>ξ<sub>y</sub></i></span> in the direction of the assigned <span class="texhtml"><i>V</i><sub>H</sub></span>. <span class="texhtml"><i>V</i><sub>H</sub></span> is negative for some semiconductors where "holes" appear to flow. In steady-state, <span class="texhtml"><i>ξ<sub>y</sub></i></span> will be strong enough to exactly cancel out the magnetic force, thus the electrons follow the straight arrow (dashed).</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Hall_Sensor.webm/220px--Hall_Sensor.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="165" data-durationhint="46" data-mwtitle="Hall_Sensor.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Hall_Sensor.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="640" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/7/77/Hall_Sensor.webm" type="video/webm; codecs="vp8, vorbis"" data-width="640" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="192" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="320" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="480" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="480" data-height="360" /></video></span><figcaption>The animation shows the action of a magnetic field on a beam of electric charges in vacuum, or in other terms, exclusively the action of the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a>. This animation is an illustration of a typical error performed in the framework of the interpretation of the Hall effect. Indeed, at stationary regime and inside a Hall-bar, the electric current is longitudinal whatever the magnetic field and there is no transverse current <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {j_{y}=0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {j_{y}=0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad9bb256304d12281826919a854d1bfc6adda523" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.027ex; width:6.295ex; height:2.843ex;" alt="{\displaystyle {j_{y}=0}}"></span> (in contrast to the case of the corbino disc). Only the electric field is modified by a transverse component <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {E_{y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {E_{y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2fec8c85159e937506748e99a366a736fbf321d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.765ex; height:2.843ex;" alt="{\displaystyle {E_{y}}}"></span>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>For a simple metal where there is only one type of <a href="/wiki/Charge_carrier" title="Charge carrier">charge carrier</a> (electrons), the Hall voltage <span class="texhtml"><i>V</i><sub>H</sub></span> can be derived by using the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a> and seeing that, in the steady-state condition, charges are not moving in the <span class="texhtml"><i>y</i></span>-axis direction. Thus, the magnetic force on each electron in the <span class="texhtml"><i>y</i></span>-axis direction is cancelled by a <span class="texhtml"><i>y</i></span>-axis electrical force due to the buildup of charges. The <span class="texhtml"><i>v<sub>x</sub></i></span> term is the <a href="/wiki/Drift_velocity" title="Drift velocity">drift velocity</a> of the current which is assumed at this point to be holes by convention. The <span class="texhtml"><i>v<sub>x</sub>B<sub>z</sub></i></span> term is negative in the <span class="texhtml"><i>y</i></span>-axis direction by the right hand rule. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =q{\bigl (}\mathbf {E} +\mathbf {v} \times \mathbf {B} {\bigl )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>=</mo> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} =q{\bigl (}\mathbf {E} +\mathbf {v} \times \mathbf {B} {\bigl )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb5174eae4771fdc515ce6d73757c391748289f1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.73ex; height:3.176ex;" alt="{\displaystyle \mathbf {F} =q{\bigl (}\mathbf {E} +\mathbf {v} \times \mathbf {B} {\bigl )}}"></span> </p><p>In steady state, <span class="texhtml"><b>F</b> = <b>0</b></span>, so <span class="texhtml">0 = <i>E<sub>y</sub></i> − <i>v<sub>x</sub>B<sub>z</sub></i></span>, where <span class="texhtml"><i>E<sub>y</sub></i></span> is assigned in the direction of the <span class="texhtml"><i>y</i></span>-axis, (and not with the arrow of the induced electric field <span class="texhtml"><i>ξ<sub>y</sub></i></span> as in the image (pointing in the <span class="texhtml">−<i>y</i></span> direction), which tells you where the field caused by the electrons is pointing). </p><p>In wires, electrons instead of holes are flowing, so <span class="texhtml"><i>v<sub>x</sub></i> → −<i>v<sub>x</sub></i></span> and <span class="texhtml"><i>q</i> → −<i>q</i></span>. Also <span class="texhtml"><i>E<sub>y</sub></i> = −<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><i>V</i><sub>H</sub></span><span class="sr-only">/</span><span class="den"><i>w</i></span></span>⁠</span></span>. Substituting these changes gives </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\mathrm {H} }=v_{x}B_{z}w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\mathrm {H} }=v_{x}B_{z}w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f54f7989647a833a7a104035165453ef68ba3825" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.648ex; height:2.509ex;" alt="{\displaystyle V_{\mathrm {H} }=v_{x}B_{z}w}"></span> </p><p>The conventional "hole" current is in the negative direction of the electron current and the negative of the electrical charge which gives <span class="texhtml"><i>I<sub>x</sub></i> = <i>ntw</i>(−<i>v<sub>x</sub></i>)(−<i>e</i>)</span> where <span class="texhtml"><i>n</i></span> is <a href="/wiki/Charge_carrier_density" title="Charge carrier density">charge carrier density</a>, <span class="texhtml"><i>tw</i></span> is the cross-sectional area, and <span class="texhtml">−<i>e</i></span> is the charge of each electron. Solving for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span> and plugging into the above gives the Hall voltage: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{\mathrm {H} }={\frac {I_{x}B_{z}}{nte}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi>n</mi> <mi>t</mi> <mi>e</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{\mathrm {H} }={\frac {I_{x}B_{z}}{nte}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e67508d2250758f0e63fbbd755ea45dee81ef0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.716ex; height:5.176ex;" alt="{\displaystyle V_{\mathrm {H} }={\frac {I_{x}B_{z}}{nte}}}"></span> </p><p>If the charge build up had been positive (as it appears in some metals and semiconductors), then the <span class="texhtml"><i>V</i><sub>H</sub></span> assigned in the image would have been negative (positive charge would have built up on the left side). </p><p>The Hall coefficient is defined as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B_{z}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B_{z}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87917f744e113455c8e2f94bbb86592ba33fc3fc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.06ex; height:6.009ex;" alt="{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B_{z}}}}"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {E} =-R_{\mathrm {H} }(\mathbf {J} _{c}\times \mathbf {B} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> </mrow> <mo>=</mo> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">J</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">B</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {E} =-R_{\mathrm {H} }(\mathbf {J} _{c}\times \mathbf {B} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc4aabf136a3c8dca78e6c4390b6c4dbb216c3d3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.768ex; height:2.843ex;" alt="{\displaystyle \mathbf {E} =-R_{\mathrm {H} }(\mathbf {J} _{c}\times \mathbf {B} )}"></span> where <span class="texhtml mvar" style="font-style:italic;">j</span> is the <a href="/wiki/Current_density" title="Current density">current density</a> of the carrier electrons, and <span class="texhtml"><i>E<sub>y</sub></i></span> is the induced electric field. In SI units, this becomes <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B}}={\frac {V_{\mathrm {H} }t}{IB}}={\frac {1}{ne}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mrow> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mi>t</mi> </mrow> <mrow> <mi>I</mi> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mi>e</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B}}={\frac {V_{\mathrm {H} }t}{IB}}={\frac {1}{ne}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5723005966da73eb6053d3c9e44b60dc29dbda8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.712ex; height:6.009ex;" alt="{\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B}}={\frac {V_{\mathrm {H} }t}{IB}}={\frac {1}{ne}}.}"></span> </p><p>(The units of <span class="texhtml"><i>R</i><sub>H</sub></span> are usually expressed as m<sup>3</sup>/C, or Ω·cm/<a href="/wiki/Gauss_(unit)" title="Gauss (unit)">G</a>, or other variants.) As a result, the Hall effect is very useful as a means to measure either the carrier density or the magnetic field. </p><p>One very important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. In the diagram above, the Hall effect with a negative <a href="/wiki/Charge_carrier" title="Charge carrier">charge carrier</a> (the electron) is presented. But consider the same magnetic field and current are applied but the current is carried inside the Hall effect device by a positive particle. The particle would of course have to be moving in the opposite direction of the electron in order for the current to be the same—down in the diagram, not up like the electron is. And thus, mnemonically speaking, your thumb in the <a href="/wiki/File:Regla_mano_derecha_Laplace.svg" title="File:Regla mano derecha Laplace.svg">Lorentz force law</a>, representing (conventional) current, would be pointing the <i>same</i> direction as before, because current is the same—an electron moving up is the same current as a positive charge moving down. And with the fingers (magnetic field) also being the same, interestingly <i>the charge carrier gets deflected to the left in the diagram regardless of whether it is positive or negative.</i> But if positive carriers are deflected to the left, they would build a relatively <i>positive voltage</i> on the left whereas if negative carriers (namely electrons) are, they build up a negative voltage on the left as shown in the diagram. Thus for the same current and magnetic field, the <a href="/wiki/Electric_polarity" class="mw-redirect" title="Electric polarity">electric polarity</a> of the Hall voltage is dependent on the internal nature of the conductor and is useful to elucidate its inner workings. </p><p>This property of the Hall effect offered the first real proof that electric currents in most metals are carried by moving electrons, not by protons. It also showed that in some substances (especially <a href="/wiki/P-type_semiconductor" class="mw-redirect" title="P-type semiconductor">p-type semiconductors</a>), it is contrarily more appropriate to think of the current as positive "<a href="/wiki/Electron_hole" title="Electron hole">holes</a>" moving rather than negative electrons. A common source of confusion with the Hall effect in such materials is that holes moving one way are really electrons moving the opposite way, so one expects the Hall voltage polarity to be the same as if electrons were the <a href="/wiki/Charge_carriers" class="mw-redirect" title="Charge carriers">charge carriers</a> as in most metals and <a href="/wiki/N-type_semiconductor" class="mw-redirect" title="N-type semiconductor">n-type semiconductors</a>. Yet we observe the opposite polarity of Hall voltage, indicating positive charge carriers. However, of course there are no actual <a href="/wiki/Positrons" class="mw-redirect" title="Positrons">positrons</a> or other positive <a href="/wiki/Elementary_particle" title="Elementary particle">elementary particles</a> carrying the charge in <a href="/wiki/P-type_semiconductor" class="mw-redirect" title="P-type semiconductor">p-type semiconductors</a>, hence the name "holes". In the same way as the oversimplistic picture of light in glass as photons being absorbed and re-emitted to explain <a href="/wiki/Refraction" title="Refraction">refraction</a> breaks down upon closer scrutiny, this apparent contradiction too can only be resolved by the modern quantum mechanical theory of <a href="/wiki/Quasiparticles" class="mw-redirect" title="Quasiparticles">quasiparticles</a> wherein the collective quantized motion of multiple particles can, in a real physical sense, be considered to be a particle in its own right (albeit not an elementary one).<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Unrelatedly, inhomogeneity in the conductive sample can result in a spurious sign of the Hall effect, even in ideal <a href="/wiki/Van_der_Pauw_method" title="Van der Pauw method">van der Pauw</a> configuration of electrodes. For example, a Hall effect consistent with positive carriers was observed in evidently n-type semiconductors.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Another source of artefact, in uniform materials, occurs when the sample's aspect ratio is not long enough: the full Hall voltage only develops far away from the current-introducing contacts, since at the contacts the transverse voltage is shorted out to zero. </p> <div class="mw-heading mw-heading3"><h3 id="Hall_effect_in_semiconductors">Hall effect in semiconductors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=5" title="Edit section: Hall effect in semiconductors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When a current-carrying <a href="/wiki/Semiconductor" title="Semiconductor">semiconductor</a> is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges. </p><p>The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single <a href="/wiki/Charge_carrier" title="Charge carrier">charge carrier</a>. However, in semiconductors and many metals the theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> and <a href="/wiki/Electron_hole" title="Electron hole">holes</a>, which may be present in different concentrations and have different <a href="/wiki/Electron_mobility" title="Electron mobility">mobilities</a>. For moderate magnetic fields the Hall coefficient is<sup id="cite_ref-Kasap2001_15-0" class="reference"><a href="#cite_note-Kasap2001-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {H} }={\frac {p\mu _{\mathrm {h} }^{2}-n\mu _{\mathrm {e} }^{2}}{e(p\mu _{\mathrm {h} }+n\mu _{\mathrm {e} })^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>p</mi> <msubsup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <mi>n</mi> <msubsup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mrow> <mi>e</mi> <mo stretchy="false">(</mo> <mi>p</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> <mo>+</mo> <mi>n</mi> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {H} }={\frac {p\mu _{\mathrm {h} }^{2}-n\mu _{\mathrm {e} }^{2}}{e(p\mu _{\mathrm {h} }+n\mu _{\mathrm {e} })^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21348a6be48946d282e3d8ed203c07cc140072a7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.427ex; height:6.843ex;" alt="{\displaystyle R_{\mathrm {H} }={\frac {p\mu _{\mathrm {h} }^{2}-n\mu _{\mathrm {e} }^{2}}{e(p\mu _{\mathrm {h} }+n\mu _{\mathrm {e} })^{2}}}}"></span> or equivalently <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\mathrm {H} }={\frac {p-nb^{2}}{e(p+nb)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>p</mi> <mo>−</mo> <mi>n</mi> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>e</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>+</mo> <mi>n</mi> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {H} }={\frac {p-nb^{2}}{e(p+nb)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4818410cb8dd83351bce79f32be9411a65590987" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:17.513ex; height:6.509ex;" alt="{\displaystyle R_{\mathrm {H} }={\frac {p-nb^{2}}{e(p+nb)^{2}}}}"></span> with <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b={\frac {\mu _{\mathrm {e} }}{\mu _{\mathrm {h} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">h</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\frac {\mu _{\mathrm {e} }}{\mu _{\mathrm {h} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20ef96a7fa13fead11b6448d6284630690d057c7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.127ex; height:5.343ex;" alt="{\displaystyle b={\frac {\mu _{\mathrm {e} }}{\mu _{\mathrm {h} }}}.}"></span> Here <span class="texhtml"><i>n</i></span> is the electron concentration, <span class="texhtml"><i>p</i></span> the hole concentration, <span class="texhtml"><i>μ</i><sub>e</sub></span> the electron mobility, <span class="texhtml"><i>μ</i><sub>h</sub></span> the hole mobility and <span class="texhtml"><i>e</i></span> the elementary charge. </p><p>For large applied fields the simpler expression analogous to that for a single carrier type holds. </p> <div class="mw-heading mw-heading3"><h3 id="Relationship_with_star_formation">Relationship with star formation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=6" title="Edit section: Relationship with star formation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Although it is well known that magnetic fields play an important role in star formation, research models<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> indicate that Hall diffusion critically influences the dynamics of gravitational collapse that forms protostars. </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_Hall_effect">Quantum Hall effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=7" title="Edit section: Quantum Hall effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></div> <p>For a two-dimensional electron system which can be produced in a <a href="/wiki/MOSFET" title="MOSFET">MOSFET</a>, in the presence of large <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a> strength and low <a href="/wiki/Temperature" title="Temperature">temperature</a>, one can observe the quantum Hall effect, in which the Hall <a href="/wiki/Electrical_conductance" class="mw-redirect" title="Electrical conductance">conductance</a> <span class="texhtml mvar" style="font-style:italic;">σ</span> undergoes <a href="/wiki/Quantum_Hall_transitions" title="Quantum Hall transitions">quantum Hall transitions</a> to take on the quantized values. </p> <div class="mw-heading mw-heading3"><h3 id="Spin_Hall_effect">Spin Hall effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=8" title="Edit section: Spin Hall effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></div> <p>The spin Hall effect consists in the spin accumulation on the lateral boundaries of a current-carrying sample. No magnetic field is needed. It was predicted by <a href="/wiki/Mikhail_Dyakonov" title="Mikhail Dyakonov">Mikhail Dyakonov</a> and <a href="/w/index.php?title=V._I._Perel&action=edit&redlink=1" class="new" title="V. I. Perel (page does not exist)">V. I. Perel</a> in 1971 and observed experimentally more than 30 years later, both in semiconductors and in metals, at cryogenic as well as at room temperatures. </p><p>The quantity describing the strength of the Spin Hall effect is known as Spin Hall angle, and it is defined as: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{SH}={\frac {2e}{\hbar }}{\frac {|j_{s}|}{|j_{e}|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mi>H</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>e</mi> </mrow> <mi class="MJX-variant">ℏ</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta _{SH}={\frac {2e}{\hbar }}{\frac {|j_{s}|}{|j_{e}|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/493d2402303589b9ae408858b1c0c99cead33984" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.114ex; height:6.509ex;" alt="{\displaystyle \theta _{SH}={\frac {2e}{\hbar }}{\frac {|j_{s}|}{|j_{e}|}}}"></span> </p><p>Where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j_{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30e60e2017a152041df43af883366c5ae2b74ca8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:1.988ex; height:2.509ex;" alt="{\displaystyle j_{s}}"></span> is the spin current generated by the applied current density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>j</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a48b3c62d86d8c5cc5675ea6e000cda05ee0f20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:1.983ex; height:2.509ex;" alt="{\displaystyle j_{e}}"></span>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Quantum_spin_Hall_effect">Quantum spin Hall effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=9" title="Edit section: Quantum spin Hall effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Quantum_spin_Hall_effect" title="Quantum spin Hall effect">Quantum spin Hall effect</a></div> <p>For <a href="/wiki/Mercury_telluride" title="Mercury telluride">mercury telluride</a> two dimensional quantum wells with strong spin-orbit coupling, in zero magnetic field, at low temperature, the quantum spin Hall effect has been observed in 2007.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Anomalous_Hall_effect">Anomalous Hall effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=10" title="Edit section: Anomalous Hall effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Ferromagnetism" title="Ferromagnetism">ferromagnetic</a> materials (and <a href="/wiki/Paramagnetism" title="Paramagnetism">paramagnetic</a> materials in a <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>), the Hall resistivity includes an additional contribution, known as the <b>anomalous Hall effect</b> (or the <b>extraordinary Hall effect</b>), which depends directly on the <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> of the material, and is often much larger than the ordinary Hall effect. (Note that this effect is <i>not</i> due to the contribution of the <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> to the total <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic field</a>.) For example, in nickel, the anomalous Hall coefficient is about 100 times larger than the ordinary Hall coefficient near the Curie temperature, but the two are similar at very low temperatures.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Although a well-recognized phenomenon, there is still debate about its origins in the various materials. The anomalous Hall effect can be either an <i>extrinsic</i> (disorder-related) effect due to <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>-dependent <a href="/wiki/Scattering" title="Scattering">scattering</a> of the <a href="/wiki/Charge_carrier" title="Charge carrier">charge carriers</a>, or an <i>intrinsic</i> effect which can be described in terms of the <a href="/wiki/Geometric_phase" title="Geometric phase">Berry phase</a> effect in the crystal momentum space (<span class="texhtml"><i>k</i></span>-space).<sup id="cite_ref-sinitsyn-08jpa_23-0" class="reference"><a href="#cite_note-sinitsyn-08jpa-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hall_effect_in_ionized_gases">Hall effect in ionized gases</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=11" title="Edit section: Hall effect in ionized gases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Hall effect in an ionized gas (<a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a>) is significantly different from the Hall effect in solids (where the <b>Hall parameter</b> is always much less than unity). In a plasma, the Hall parameter can take any value. The Hall parameter, <span class="texhtml"><i>β</i></span>, in a plasma is the ratio between the electron <a href="/wiki/Gyroradius" title="Gyroradius">gyrofrequency</a>, <span class="texhtml"><i>Ω</i><sub>e</sub></span>, and the electron-heavy particle collision frequency, <span class="texhtml mvar" style="font-style:italic;">ν</span>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta ={\frac {\Omega _{\mathrm {e} }}{\nu }}={\frac {eB}{m_{\mathrm {e} }\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mi>ν</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>e</mi> <mi>B</mi> </mrow> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mi>ν</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {\Omega _{\mathrm {e} }}{\nu }}={\frac {eB}{m_{\mathrm {e} }\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cd5a54254e080adab199cc7c7ed5774dba49fd0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.076ex; height:5.676ex;" alt="{\displaystyle \beta ={\frac {\Omega _{\mathrm {e} }}{\nu }}={\frac {eB}{m_{\mathrm {e} }\nu }}}"></span> where </p> <ul><li><span class="texhtml"><i>e</i></span> is the <a href="/wiki/Elementary_charge" title="Elementary charge">elementary charge</a> (approximately <span class="nowrap"><span data-sort-value="6981160000000000000♠"></span>1.6<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−19</sup> <a href="/wiki/Coulomb" title="Coulomb">C</a></span>)</li> <li><span class="texhtml"><i>B</i></span> is the magnetic field (in <a href="/wiki/Tesla_(unit)" title="Tesla (unit)">teslas</a>)</li> <li><span class="texhtml"><i>m</i><sub>e</sub></span> is the <a href="/wiki/Electron" title="Electron">electron mass</a> (approximately <span class="nowrap"><span data-sort-value="6969910000000000000♠"></span>9.1<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−31</sup> kg</span>).</li></ul> <p>The Hall parameter value increases with the magnetic field strength. </p><p>Physically, the trajectories of electrons are curved by the <a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a>. Nevertheless, when the Hall parameter is low, their motion between two encounters with heavy particles (<a href="/wiki/Neutral_particle" title="Neutral particle">neutral</a> or <a href="/wiki/Ion" title="Ion">ion</a>) is almost linear. But if the Hall parameter is high, the electron movements are highly curved. The <a href="/wiki/Current_density" title="Current density">current density</a> vector, <span class="texhtml"><b>J</b></span>, is no longer collinear with the <a href="/wiki/Electric_field" title="Electric field">electric field</a> vector, <span class="texhtml"><b>E</b></span>. The two vectors <span class="texhtml"><b>J</b></span> and <span class="texhtml"><b>E</b></span> make the <b>Hall angle</b>, <span class="texhtml mvar" style="font-style:italic;">θ</span>, which also gives the Hall parameter: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =\tan(\theta ).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =\tan(\theta ).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f22ba597d57743d21a123c4cae5be17b7a5748e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.337ex; height:2.843ex;" alt="{\displaystyle \beta =\tan(\theta ).}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Other_Hall_effects">Other Hall effects</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=12" title="Edit section: Other Hall effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Hall Effects family has expanded to encompass other quasi-particles in semiconductor nanostructures. Specifically, a set of Hall Effects has emerged based on excitons<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> and exciton-polaritons<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> n 2D materials and quantum wells. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=13" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hall_effect_sensor" title="Hall effect sensor">Hall effect sensor</a></div> <p><a href="/wiki/Hall_sensors" class="mw-redirect" title="Hall sensors">Hall sensors</a> amplify and use the Hall effect for a variety of sensing applications. </p> <div class="mw-heading mw-heading2"><h2 id="Corbino_effect">Corbino effect</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=14" title="Edit section: Corbino effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Corbino_disc_by_Zureks.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Corbino_disc_by_Zureks.svg/200px-Corbino_disc_by_Zureks.svg.png" decoding="async" width="200" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Corbino_disc_by_Zureks.svg/300px-Corbino_disc_by_Zureks.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Corbino_disc_by_Zureks.svg/400px-Corbino_disc_by_Zureks.svg.png 2x" data-file-width="320" data-file-height="360" /></a><figcaption>Corbino disc – dashed curves represent <a href="/wiki/Logarithmic_spiral" title="Logarithmic spiral">logarithmic spiral</a> paths of deflected electrons</figcaption></figure> <p>The Corbino effect, named after its discoverer <a href="/wiki/Orso_Mario_Corbino" title="Orso Mario Corbino">Orso Mario Corbino</a>, is a phenomenon involving the Hall effect, but a disc-shaped metal sample is used in place of a rectangular one. Because of its shape the Corbino disc allows the observation of Hall effect–based <a href="/wiki/Magnetoresistance" title="Magnetoresistance">magnetoresistance</a> without the associated Hall voltage. </p><p>A radial current through a circular disc, subjected to a magnetic field perpendicular to the plane of the disc, produces a "circular" current through the disc.<sup id="cite_ref-Adams1915_27-0" class="reference"><a href="#cite_note-Adams1915-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>The absence of the free transverse boundaries renders the interpretation of the Corbino effect simpler than that of the Hall effect. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> 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effect">Thermal Hall effect</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="hallpdf" class="citation journal cs1"><a href="/wiki/Edwin_Hall" title="Edwin Hall">Edwin Hall</a> (1879). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110727010116/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html">"On a New Action of the Magnet on Electric Currents"</a>. <i>American Journal of Mathematics</i>. <b>2</b> (3): 287–92. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2369245">10.2307/2369245</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2369245">2369245</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:107500183">107500183</a>. Archived from <a rel="nofollow" class="external text" href="http://www.stenomuseet.dk/skoletj/elmag/kilde9.html">the original</a> on 2011-07-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-02-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Mathematics&rft.atitle=On+a+New+Action+of+the+Magnet+on+Electric+Currents&rft.volume=2&rft.issue=3&rft.pages=287-92&rft.date=1879&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A107500183%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2369245%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2369245&rft.au=Edwin+Hall&rft_id=http%3A%2F%2Fwww.stenomuseet.dk%2Fskoletj%2Felmag%2Fkilde9.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/Hall-effect">"Hall effect | Definition & Facts"</a>. <i>Encyclopedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-02-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+Britannica&rft.atitle=Hall+effect+%7C+Definition+%26+Facts&rft_id=https%3A%2F%2Fwww.britannica.com%2Fscience%2FHall-effect&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></span> </li> <li id="cite_note-:1-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRamsden2011" class="citation book cs1">Ramsden, Edward (2011-04-01). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=R8VAjMitH1QC"><i>Hall-Effect Sensors: Theory and Application</i></a>. 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(1879). <a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2369245">"On a New Action of the Magnet on Electric Currents"</a>. <i>American Journal of Mathematics</i>. <b>2</b> (3). JSTOR: 287–292. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2369245">10.2307/2369245</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9327">0002-9327</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2369245">2369245</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Mathematics&rft.atitle=On+a+New+Action+of+the+Magnet+on+Electric+Currents&rft.volume=2&rft.issue=3&rft.pages=287-292&rft.date=1879&rft.issn=0002-9327&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2369245%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2369245&rft.aulast=Hall&rft.aufirst=E.+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.2307%252F2369245&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150529002229/http://phareselectronics.com/products/hall-effect-sensors/hall-effect-history">"Hall Effect History"</a>. 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(1994-03-07). <a rel="nofollow" class="external text" href="http://aip.scitation.org/doi/10.1063/1.110859">"Hall effect under null current conditions"</a>. <i>Applied Physics Letters</i>. <b>64</b> (10): 1262–1264. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ApPhL..64.1262M">1994ApPhL..64.1262M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.110859">10.1063/1.110859</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0003-6951">0003-6951</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Physics+Letters&rft.atitle=Hall+effect+under+null+current+conditions&rft.volume=64&rft.issue=10&rft.pages=1262-1264&rft.date=1994-03-07&rft.issn=0003-6951&rft_id=info%3Adoi%2F10.1063%2F1.110859&rft_id=info%3Abibcode%2F1994ApPhL..64.1262M&rft.aulast=Mani&rft.aufirst=R.+G.&rft.au=von+Klitzing%2C+K.&rft_id=http%3A%2F%2Faip.scitation.org%2Fdoi%2F10.1063%2F1.110859&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=DE4308375">DE Patent 4308375</a></span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=4308375&rft.cc=DE&rft.title="><span style="display: none;"> </span></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm">"The Hall Effect"</a>. <a href="/wiki/NIST" class="mw-redirect" title="NIST">NIST</a>. 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P. (1915). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OFYLAAAAIAAJ&pg=PA47"><i>The Hall and Corbino effects</i></a>. Vol. 54. pp. 47–51. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1916PhDT.........2C">1916PhDT.........2C</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4223-7256-2" title="Special:BookSources/978-1-4223-7256-2"><bdi>978-1-4223-7256-2</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-01-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Hall+and+Corbino+effects&rft.pages=47-51&rft.date=1915&rft_id=info%3Abibcode%2F1916PhDT.........2C&rft.isbn=978-1-4223-7256-2&rft.aulast=Adams&rft.aufirst=E.+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOFYLAAAAIAAJ%26pg%3DPA47&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment"><code class="cs1-code">|journal=</code> ignored (<a href="/wiki/Help:CS1_errors#periodical_ignored" title="Help:CS1 errors">help</a>)</span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=17" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Introduction to Plasma Physics and Controlled Fusion, Volume 1, Plasma Physics, Second Edition, 1984, Francis F. Chen</li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=18" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaumgartnerIhnEnsslinPapp2006" class="citation journal cs1">Baumgartner, A.; Ihn, T.; Ensslin, K.; Papp, G.; Peeters, F.; Maranowski, K.; Gossard, A. C. (2006). <a rel="nofollow" class="external text" href="https://repository.uantwerpen.be/docman/irua/df27b2/61360.pdf">"Classical Hall effect in scanning gate experiments"</a> <span class="cs1-format">(PDF)</span>. <i>Physical Review B</i>. <b>74</b> (16): 165426. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006PhRvB..74p5426B">2006PhRvB..74p5426B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevB.74.165426">10.1103/PhysRevB.74.165426</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10067%2F613600151162165141">10067/613600151162165141</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+B&rft.atitle=Classical+Hall+effect+in+scanning+gate+experiments&rft.volume=74&rft.issue=16&rft.pages=165426&rft.date=2006&rft_id=info%3Ahdl%2F10067%2F613600151162165141&rft_id=info%3Adoi%2F10.1103%2FPhysRevB.74.165426&rft_id=info%3Abibcode%2F2006PhRvB..74p5426B&rft.aulast=Baumgartner&rft.aufirst=A.&rft.au=Ihn%2C+T.&rft.au=Ensslin%2C+K.&rft.au=Papp%2C+G.&rft.au=Peeters%2C+F.&rft.au=Maranowski%2C+K.&rft.au=Gossard%2C+A.+C.&rft_id=https%3A%2F%2Frepository.uantwerpen.be%2Fdocman%2Firua%2Fdf27b2%2F61360.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></li> <li>Annraoi M. de Paor. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304065302/http://gcdcc.hebut.edu.cn/ydzl/19-Correction%20to%20the%20classical%20two-species%20Hall%20Coefficient%20using%20twoport%20network%20theory.pdf"><i>Correction to the classical two-species Hall Coefficient using twoport network theory</i></a>. International Journal of Electrical Engineering Education 43/4.</li> <li><a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/III_14.html#Ch14-S3">The Hall effect - The Feynman Lectures on Physics</a></li> <li>University of Washington <a rel="nofollow" class="external text" href="http://courses.washington.edu/phys431/hall_effect/hall_effect.pdf">The Hall Effect</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hall_effect&action=edit&section=19" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US1778796">U.S. patent 1,778,796</a></span>, P. H. Craig, <i>System and apparatus employing the Hall effect</i></li> <li><span><a rel="nofollow" class="external text" href="https://patents.google.com/patent/US3596114">U.S. patent 3,596,114</a></span>, J. T. Maupin, E. A. Vorthmann, <i>Hall effect contactless switch with prebiased Schmitt trigger</i></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1041539562"><span class="citation patent" id="CITEREFR._G._ManiK._von_Klitzing"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US5646527">US Patent 5646527</a>, R. G. Mani & K. von Klitzing, "Hall-effect device with current and Hall-voltage connections"</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=5646527&rft.cc=US&rft.title=Hall-effect+device+with+current+and+Hall-voltage+connections&rft.inventor=R.+G.+Mani"><span style="display: none;"> </span></span></li> <li><a rel="nofollow" class="external text" href="http://www.allaboutcircuits.com/technical-articles/understanding-and-applying-the-hall-effect/">Understanding and Applying the Hall Effect</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160104220005/http://www.alta-space.com/index.php?page=hall-effect-thrusters">Hall Effect Thrusters</a> Alta Space</li> <li><a rel="nofollow" class="external text" href="http://www.fxsolver.com/solve/share/xZGOEQABCTLZvFU08CT9Pg==/">Hall effect calculators</a></li> <li><a rel="nofollow" class="external text" href="https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect">Interactive Java tutorial on the Hall effect</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200709054706/https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect">Archived</a> 2020-07-09 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> National High Magnetic Field Laboratory</li> <li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/HallEffect.html">Science World (wolfram.com)</a> article.</li> <li>"<a rel="nofollow" class="external text" href="https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm">The Hall Effect</a>". nist.gov.</li> <li><a rel="nofollow" class="external text" href="http://it.stlawu.edu/~koon/HallTable.html">Table with Hall coefficients of different elements at room temperature</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141221212222/http://it.stlawu.edu/~koon/HallTable.html">Archived</a> 2014-12-21 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=poqe8Vn5AiQ">Simulation of the Hall effect as a Youtube video</a></li> <li><a rel="nofollow" class="external text" href="http://scitation.aip.org/content/aip/journal/jcp/87/1/10.1063/1.453559">Hall effect in electrolytes</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBowley2010" class="citation web cs1">Bowley, Roger (2010). <a rel="nofollow" class="external text" href="http://www.sixtysymbols.com/videos/halleffect.htm">"Hall Effect"</a>. <i>Sixty Symbols</i>. <a href="/wiki/Brady_Haran" title="Brady Haran">Brady Haran</a> for the <a href="/wiki/University_of_Nottingham" title="University of Nottingham">University of Nottingham</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Sixty+Symbols&rft.atitle=Hall+Effect&rft.date=2010&rft.aulast=Bowley&rft.aufirst=Roger&rft_id=http%3A%2F%2Fwww.sixtysymbols.com%2Fvideos%2Fhalleffect.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHall+effect" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output 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scope="row" class="navbox-group" style="width:1%"><a href="/wiki/State_of_matter" title="State of matter">States of matter</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Solid" title="Solid">Solid</a></li> <li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li> <li><a href="/wiki/Gas" title="Gas">Gas</a></li> <li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li> <li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li> <li><a href="/wiki/Fermi_gas" title="Fermi gas">Fermi gas</a></li> <li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li> <li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluid</a></li> <li><a href="/wiki/Luttinger_liquid" title="Luttinger liquid">Luttinger liquid</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:QuantumPhaseTransition.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/220px-QuantumPhaseTransition.svg.png" decoding="async" width="220" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/330px-QuantumPhaseTransition.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/QuantumPhaseTransition.svg/440px-QuantumPhaseTransition.svg.png 2x" data-file-width="512" data-file-height="369" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phase phenomena</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Order_parameter" class="mw-redirect" title="Order parameter">Order parameter</a></li> <li><a href="/wiki/Phase_transition" title="Phase transition">Phase transition</a></li> <li><a href="/wiki/Spontaneous_symmetry_breaking" title="Spontaneous symmetry breaking">Spontaneous symmetry breaking</a></li> <li><a href="/wiki/Critical_phenomena" title="Critical phenomena">Critical phenomena</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Electrons in solids</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Hall effect</a></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall effect</a></li> <li><a href="/wiki/Spin_Hall_effect" title="Spin Hall effect">Spin Hall effect</a></li> <li><a href="/wiki/Quantum_spin_Hall_effect" title="Quantum spin Hall effect">Quantum spin Hall effect</a></li> <li><a href="/wiki/Berry_phase" class="mw-redirect" title="Berry phase">Berry phase</a></li> <li><a href="/wiki/Aharonov%E2%80%93Bohm_effect" title="Aharonov–Bohm effect">Aharonov–Bohm effect</a></li> <li><a href="/wiki/Josephson_effect" title="Josephson effect">Josephson effect</a></li> <li><a href="/wiki/Kondo_effect" title="Kondo effect">Kondo effect</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Drude_model" title="Drude model">Drude model</a></li> <li><a href="/wiki/Free_electron_model" title="Free electron model">Free electron model</a></li> <li><a href="/wiki/Nearly_free_electron_model" title="Nearly free electron model">Nearly free electron model</a></li> <li><a href="/wiki/Bloch%27s_theorem" title="Bloch's theorem">Bloch's theorem</a></li> <li><a href="/wiki/Fermi_liquid_theory" title="Fermi liquid theory">Fermi liquid theory</a></li> <li><a href="/wiki/Electronic_band_structure" title="Electronic band structure">electronic band structure</a></li> <li><a href="/wiki/Anderson_localization" title="Anderson localization">Anderson localization</a></li> <li><a href="/wiki/BCS_theory" title="BCS theory">BCS theory</a></li> <li><a href="/wiki/Tight_binding_model" class="mw-redirect" title="Tight binding model">tight binding model</a></li> <li><a href="/wiki/Hubbard_model" title="Hubbard model">Hubbard model</a></li> <li><a href="/wiki/Density_functional_theory" title="Density functional theory">Density functional theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Conduction</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Mott_insulator" title="Mott insulator">Mott insulator</a></li> <li><a href="/wiki/Semiconductor" title="Semiconductor">Semiconductor</a></li> <li><a href="/wiki/Semimetal" title="Semimetal">Semimetal</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductor</a></li> <li><a href="/wiki/Topological_insulator" title="Topological insulator">Topological insulator</a></li> <li><a href="/wiki/Spin_gapless_semiconductor" title="Spin gapless semiconductor">Spin gapless semiconductor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Couplings</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Thermoelectric_effect" title="Thermoelectric effect">Thermoelectricity</a></li> <li><a href="/wiki/Piezoelectricity" title="Piezoelectricity">Piezoelectricity</a></li> <li><a href="/wiki/Ferroelectricity" title="Ferroelectricity">Ferroelectricity</a></li> <li><a href="/wiki/Flexoelectricity" title="Flexoelectricity">Flexoelectricity</a></li> <li><a href="/wiki/Electrostriction" title="Electrostriction">Electrostriction</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Magnetic phases</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amorphous_magnet" title="Amorphous magnet">Amorphous magnet</a></li> <li><a href="/wiki/Diamagnetism" title="Diamagnetism">Diamagnet</a></li> <li><a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">Superdiamagnet</a></li> <li><a href="/wiki/Paramagnetism" title="Paramagnetism">Paramagnet</a></li> <li><a href="/wiki/Superparamagnetism" title="Superparamagnetism">Superparamagnet</a></li> <li><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li> <li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a></li> <li><a href="/wiki/Metamagnetism" title="Metamagnetism">Metamagnet</a></li> <li><a href="/wiki/Spin_glass" title="Spin glass">Spin glass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quasiparticle" title="Quasiparticle">Quasiparticles</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anyon" title="Anyon">Anyon</a></li> <li><a href="/wiki/Bogoliubov_quasiparticle" title="Bogoliubov quasiparticle">Bogoliubov quasiparticle</a></li> <li><a href="/wiki/Electron_hole" title="Electron hole">Hole</a></li> <li><a href="/wiki/Exciton" title="Exciton">Exciton</a></li> <li><a href="/wiki/Magnon" title="Magnon">Magnon</a></li> <li><a href="/wiki/Phonon" title="Phonon">Phonon</a></li> <li><a href="/wiki/Pines%27_demon" title="Pines' demon">Pines' demon</a></li> <li><a href="/wiki/Plasmon" title="Plasmon">Plasmon</a></li> <li><a href="/wiki/Polariton" title="Polariton">Polariton</a> <ul><li><a href="/wiki/Exciton-polariton" title="Exciton-polariton">Exciton-polariton</a></li> <li><a href="/wiki/Phonon_polariton" title="Phonon polariton">Phonon polariton</a></li></ul></li> <li><a href="/wiki/Polaron" title="Polaron">Polaron</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Soft_matter" title="Soft matter">Soft matter</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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