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href="#Junction_experiment_supporting_the_d-wave_symmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Junction experiment supporting the <i>d-wave</i> symmetry</span> </div> </a> <ul id="toc-Junction_experiment_supporting_the_d-wave_symmetry-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">6</span> <span>References</span> </div> </a> <ul id="toc-References-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" 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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">Superconductive materials not explained by existing established theories</div> <p class="mw-empty-elt"> </p><p><b>Unconventional superconductors</b> are materials that display <a href="/wiki/Superconductivity" title="Superconductivity">superconductivity</a> which is not explained by the usual <a href="/wiki/BCS_theory" title="BCS theory">BCS theory</a> or its extension, the <a href="/w/index.php?title=Eliashberg_theory&action=edit&redlink=1" class="new" title="Eliashberg theory (page does not exist)">Eliashberg theory</a>. The pairing in unconventional superconductors may originate from some other mechanism than the electron–phonon interaction.<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> Alternatively, a superconductor is unconventional if the superconducting <a href="/wiki/Order_parameter" class="mw-redirect" title="Order parameter">order parameter</a> transforms according to a non-trivial <a href="/wiki/Irreducible_representation" title="Irreducible representation">irreducible representation</a> of the <a href="/wiki/Point_group" title="Point group">point group</a> or <a href="/wiki/Space_group" title="Space group">space group</a> of the system.<sup id="cite_ref-c718_2-0" class="reference"><a href="#cite_note-c718-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Per definition, superconductors that break additional symmetries to <i>U</i> (1) symmetry are known as unconventional superconductors.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The superconducting properties of CeCu<sub>2</sub>Si<sub>2</sub>, a type of <a href="/wiki/Heavy_fermion_material" title="Heavy fermion material">heavy fermion material</a>, were reported in 1979 by <a href="/wiki/Frank_Steglich" title="Frank Steglich">Frank Steglich</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> For a long time it was believed that CeCu<sub>2</sub>Si<sub>2</sub> was a singlet d-wave superconductor, but since the mid-2010s, this notion has been strongly contested.<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> In the early eighties, many more unconventional, <a href="/wiki/Heavy_fermion" class="mw-redirect" title="Heavy fermion">heavy fermion</a> <a href="/wiki/Superconductivity" title="Superconductivity">superconductors</a> were discovered, including UBe<sub>13</sub>,<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> <a href="/wiki/UPt3" title="UPt3">UPt<sub>3</sub></a><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> and URu<sub>2</sub>Si<sub>2</sub>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In each of these materials, the anisotropic nature of the pairing was implicated by the power-law dependence of the <a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">nuclear magnetic resonance</a> (NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt<sub>3</sub> was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.<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>The first unconventional triplet superconductor, organic material (TMTSF)<sub>2</sub>PF<sub>6</sub>, was discovered by <a href="/w/index.php?title=Denis_Jerome&action=edit&redlink=1" class="new" title="Denis Jerome (page does not exist)">Denis Jerome</a>, <a href="/wiki/Klaus_Bechgaard" title="Klaus Bechgaard">Klaus Bechgaard</a> and coworkers in 1980 (TMTSF = Tetramethyltetraselenafulvalenium, see <a href="/wiki/Fulvalene" title="Fulvalene">Fulvalene</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> Experimental works by <a href="/wiki/Paul_Chaikin" title="Paul Chaikin">Paul Chaikin</a>'s and Michael Naughton's groups as well as theoretical analysis of their data by <a href="/w/index.php?title=Andrei_Lebed&action=edit&redlink=1" class="new" title="Andrei Lebed (page does not exist)">Andrei Lebed</a> have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)<sub>2</sub>X (X=PF<sub>6</sub>, ClO<sub>4</sub>, etc.) organic materials.<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>High-temperature singlet d-wave superconductivity was discovered by <a href="/wiki/J.G._Bednorz" class="mw-redirect" title="J.G. Bednorz">J.G. Bednorz</a> and <a href="/wiki/Karl_Alexander_M%C3%BCller" class="mw-redirect" title="Karl Alexander Müller">K.A. Müller</a> in 1986, who also discovered that the <a href="/wiki/Lanthanum" title="Lanthanum">lanthanum</a>-based <a href="/wiki/Cuprate_superconductor" title="Cuprate superconductor">cuprate</a> <a href="/wiki/Perovskite" title="Perovskite">perovskite</a> material LaBaCuO<sub>4</sub> develops superconductivity at a critical temperature (<i>T</i><sub>c</sub>) of approximately 35 <a href="/wiki/Kelvin" title="Kelvin">K</a> (-238 degrees <a href="/wiki/Celsius" title="Celsius">Celsius</a>). This was well above the highest critical temperature known at the time (<i>T</i><sub>c</sub> = 23 K), and thus the new family of materials was called <a href="/wiki/High-temperature_superconductivity" title="High-temperature superconductivity">high-temperature superconductors</a>. Bednorz and Müller received the <a href="/wiki/Nobel_prize" class="mw-redirect" title="Nobel prize">Nobel prize</a> in Physics for this discovery in 1987. Since then, many other <a href="/wiki/High-temperature_superconductivity" title="High-temperature superconductivity">high-temperature superconductors</a> have been synthesized. </p><p>LSCO (La<sub>2−<i>x</i></sub>Sr<sub><i>x</i></sub>CuO<sub>4</sub>) was discovered the same year (1986). Soon after, in January 1987, <a href="/wiki/Yttrium_barium_copper_oxide" title="Yttrium barium copper oxide">yttrium barium copper oxide</a> (YBCO) was discovered to have a <i>T</i><sub>c</sub> of 90 K, the first material to achieve superconductivity above the boiling point of <a href="/wiki/Liquid_nitrogen" title="Liquid nitrogen">liquid nitrogen</a> (77 K).<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> This was highly significant from the point of view of the <a href="/wiki/Technological_applications_of_superconductivity" title="Technological applications of superconductivity">technological applications of superconductivity</a> because liquid nitrogen is far less expensive than <a href="/wiki/Liquid_helium" title="Liquid helium">liquid helium</a>, which is required to cool <a href="/wiki/Conventional_superconductor" title="Conventional superconductor">conventional superconductors</a> down to their critical temperature. In 1988 <a href="/wiki/Bismuth_strontium_calcium_copper_oxide" title="Bismuth strontium calcium copper oxide">bismuth strontium calcium copper oxide</a> (BSCCO) with <i>T</i><sub>c</sub> up to 107 K,<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> and <a href="/wiki/Thallium_barium_calcium_copper_oxide" title="Thallium barium calcium copper oxide">thallium barium calcium copper oxide</a> (TBCCO) (T=thallium) with <i>T</i><sub>c</sub> of 125 K were discovered. The current record critical temperature is about <i>T</i><sub>c</sub> = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless, at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity. </p><p>On the other hand, other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as <a href="/wiki/Strontium_ruthenate" title="Strontium ruthenate">strontium ruthenate Sr<sub>2</sub>RuO<sub>4</sub></a>, but that, like high-temperature superconductors, are unconventional in other ways. (For example, the origin of the attractive force leading to the formation of <a href="/wiki/Cooper_pair" title="Cooper pair">Cooper pairs</a> may be different from the one postulated in <a href="/wiki/BCS_theory" title="BCS theory">BCS theory</a>.) In addition to this, superconductors that have unusually high values of <i>T</i><sub>c</sub> but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of <a href="/wiki/Conventional_superconductor" title="Conventional superconductor">conventional superconductors</a> (this is suspected of <a href="/wiki/Magnesium_diboride" title="Magnesium diboride">magnesium diboride</a>, MgB<sub>2</sub>, with <i>T</i><sub>c</sub> = 39 K). Others could display more unconventional features. </p><p>In 2008 a new class that does not include copper (layered <a href="/wiki/Oxypnictide" title="Oxypnictide">oxypnictide</a> superconductors), for example LaOFeAs, was discovered.<sup id="cite_ref-Superconductivity_14-0" class="reference"><a href="#cite_note-Superconductivity-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-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> An oxypnictide of <a href="/wiki/Samarium" title="Samarium">samarium</a> seemed to have a <i>T</i><sub>c</sub> of about 43 K, which was higher than predicted by BCS theory.<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> Tests at up to 45 <a href="/wiki/Tesla_(unit)" title="Tesla (unit)">T</a><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> suggested the upper critical field of LaFeAsO<sub>0.89</sub>F<sub>0.11</sub> to be around 64 T. Some other <a href="/wiki/Iron-based_superconductor" title="Iron-based superconductor">iron-based superconductors</a> do not contain oxygen. </p><p>As of 2009<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Unconventional_superconductor&action=edit">[update]</a></sup>, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub><i>x</i></sub>), at 138 K and is held by a cuprate-perovskite material,<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> possibly 164 K under high pressure.<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><p>Other unconventional superconductors not based on cuprate structure have too been found.<sup id="cite_ref-Superconductivity_14-1" class="reference"><a href="#cite_note-Superconductivity-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Some have unusually high values of the <a href="/wiki/Critical_temperature" class="mw-redirect" title="Critical temperature">critical temperature</a>, <i>T</i><sub>c</sub>, and hence they are sometimes also called high-temperature superconductors. </p> <div class="mw-heading mw-heading3"><h3 id="Graphene">Graphene</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=2" title="Edit section: Graphene"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2017, <a href="/wiki/Scanning_tunneling_microscope" title="Scanning tunneling microscope">scanning tunneling microscopy</a> and spectroscopy experiments on <a href="/wiki/Graphene" title="Graphene">graphene</a> proximitized to the electron-doped (non-chiral) <i>d</i>-wave superconductor Pr<sub>2−<i>x</i></sub>Ce<sub><i>x</i></sub>CuO<sub>4</sub> (PCCO) revealed evidence for an unconventional superconducting density of states induced in graphene.<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> Publications in March 2018 provided evidence for unconventional <a href="/wiki/Bilayer_graphene#Superconductivity_in_twisted_bilayer_graphene" title="Bilayer graphene">superconducting properties of a graphene bilayer</a> where <a href="/wiki/Twistronics" title="Twistronics">one layer was offset</a> by a "magic angle" of 1.1° relative to the other.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Ongoing_research">Ongoing research</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=3" title="Edit section: Ongoing research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While the mechanism responsible for conventional superconductivity is well described by the BCS theory,<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> the mechanism for unconventional superconductivity is still unknown. After more than twenty years of intense research, the origin of high-temperature superconductivity is still not clear, being one of the <a href="/wiki/List_of_unsolved_problems_in_physics#Condensed_matter_physics" title="List of unsolved problems in physics">major unsolved problems</a> of theoretical <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter physics</a>. It appears that unlike conventional superconductivity driven by <i>electron-phonon</i> attraction, genuine <i>electronic</i> mechanisms (such as antiferromagnetic correlations) are at play. Moreover, d-wave pairing, rather than s-wave, is significant. </p><p>One goal of much research is <a href="/wiki/Room-temperature_superconductor" title="Room-temperature superconductor">room-temperature superconductivity</a>.<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> </p><p>Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, <a href="/wiki/BSCCO" class="mw-redirect" title="BSCCO">BSCCO</a>), making theoretical modeling difficult. </p> <div class="mw-heading mw-heading2"><h2 id="Possible_mechanisms">Possible mechanisms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=4" title="Edit section: Possible mechanisms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The most controversial topic in condensed matter physics has been the mechanism for high-<i>T</i><sub>c</sub> superconductivity (HTS). There have been two representative theories on the HTS : (See also <a href="/wiki/Resonating_valence_bond_theory" title="Resonating valence bond theory">Resonating valence bond theory</a> ) </p> <div class="mw-heading mw-heading3"><h3 id="Weak-coupling_theory">Weak-coupling theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=5" title="Edit section: Weak-coupling theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Firstly, it has been suggested that the HTS emerges by antiferromagnetic spin fluctuation in a doped system.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> According to this <a href="/w/index.php?title=Weak-coupling_theory&action=edit&redlink=1" class="new" title="Weak-coupling theory (page does not exist)">weak-coupling theory</a>, the pairing wave function of the HTS should have a <i>d</i><sub><i>x</i><sup>2</sup>−<i>y</i><sup>2</sup></sub> symmetry. Thus, whether the symmetry of the pairing wave function is the <i>d</i> symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation. That is, if the HTS order parameter (pairing wave function) does not have <i>d</i> symmetry, then a pairing mechanism related to spin fluctuation can be ruled out. The <i>tunnel experiment</i> (see below) seems to detect <i>d</i> symmetry in some HTS. </p> <div class="mw-heading mw-heading3"><h3 id="Interlayer_coupling_model">Interlayer coupling model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=6" title="Edit section: Interlayer coupling model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Secondly, there is the <a href="/w/index.php?title=Interlayer_coupling_model&action=edit&redlink=1" class="new" title="Interlayer coupling model (page does not exist)">interlayer coupling model</a>, according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2020)">citation needed</span></a></i>]</sup> </p><p>In order to solve this unsettled problem, there have been numerous experiments such as photoelectron spectroscopy, NMR, specific heat measurement, etc. Unfortunately, the results were ambiguous, where some reports supported the d symmetry for the HTS but others supported the s symmetry.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2016)">citation needed</span></a></i>]</sup> This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc. </p> <div class="mw-heading mw-heading3"><h3 id="Superexchange">Superexchange</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=7" title="Edit section: Superexchange"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Promising experimental results from various researchers in September 2022, including <a href="/w/index.php?title=Weijiong_Chen&action=edit&redlink=1" class="new" title="Weijiong Chen (page does not exist)">Weijiong Chen</a>, <a href="/wiki/J._C._S%C3%A9amus_Davis" title="J. C. Séamus Davis">J.C. Séamus Davis</a> and <a href="/w/index.php?title=H._Eisiaki&action=edit&redlink=1" class="new" title="H. Eisiaki (page does not exist)">H. Eisiaki</a> revealed that <a href="/wiki/Superexchange" title="Superexchange">superexchange</a> of electrons is possibly the most probable reason for high-temperature superconductivity.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Previous_studies_on_the_symmetry_of_the_HTS_order_parameter">Previous studies on the symmetry of the HTS order parameter</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=8" title="Edit section: Previous studies on the symmetry of the HTS order parameter"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The symmetry of the HTS order parameter has been studied in <a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">nuclear magnetic resonance</a> measurements and, more recently, by <a href="/wiki/ARPES" class="mw-redirect" title="ARPES">angle-resolved photoemission</a> and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS. </p><p>NMR measurements of the resonance frequency on <a href="/wiki/YBCO" class="mw-redirect" title="YBCO">YBCO</a> indicated that electrons in the copper oxide superconductors are paired in <a href="/wiki/Singlet_state" title="Singlet state">spin-singlet</a> states. This indication came from the behavior of the <a href="/wiki/Knight_shift" title="Knight shift">Knight shift</a>, the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it. </p><p>Also, by measuring the <i>penetration depth</i>, the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/<i>k</i><sub>B</sub><i>T</i>). In that case, the penetration depth also varies exponentially with temperature <i>T</i>. If there are nodes in the energy gap as in the <i>d</i> symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially <i>d</i><sub><i>x</i><sup>2</sup>-<i>y</i><sup>2</sup></sub> then the penetration depth should vary linearly with <i>T</i> at low temperatures. This technique is increasingly being used to study superconductors and is limited in application largely by the quality of available single crystals. </p><p><a href="/wiki/Photoemission_spectroscopy" title="Photoemission spectroscopy">Photoemission spectroscopy</a> also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the <a href="/wiki/Angle-resolved_photoemission_spectroscopy" title="Angle-resolved photoemission spectroscopy">angle-resolved photoemission spectroscopy</a> (ARPES), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the <i>d</i> symmetry or not. </p> <div class="mw-heading mw-heading2"><h2 id="Junction_experiment_supporting_the_d-wave_symmetry">Junction experiment supporting the <i>d-wave</i> symmetry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unconventional_superconductor&action=edit&section=9" title="Edit section: Junction experiment supporting the d-wave symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There was a clever experimental design to overcome the muddy situation. An experiment based on pair tunneling and flux quantization in a three-grain ring of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub> (YBCO) was designed to test the symmetry of the order parameter in YBCO. <sup id="cite_ref-Tsuei1994_31-0" class="reference"><a href="#cite_note-Tsuei1994-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> Such a ring consists of three YBCO crystals with specific orientations consistent with the d-wave pairing symmetry to give rise to a spontaneously generated half-integer quantum vortex at the tricrystal meeting point. Furthermore, the possibility that junction interfaces can be in the clean limit (no defects) or with maximum zig-zag disorder was taken into account in this tricrystal experiment.<sup id="cite_ref-Tsuei1994_31-1" class="reference"><a href="#cite_note-Tsuei1994-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> A proposal of studying vortices with half magnetic flux quanta in heavy-fermion superconductors in three polycrystalline configurations was reported in 1987 by V. B. Geshkenbein, A. Larkin and A. Barone in 1987.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>In the first tricrystal pairing symmetry experiment,<sup id="cite_ref-Tsuei1994_31-2" class="reference"><a href="#cite_note-Tsuei1994-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> the spontaneous magnetization of half flux quantum was clearly observed in YBCO, which convincingly supported the <i>d-wave</i> symmetry of the order parameter in YBCO. Because YBCO is <a href="/wiki/Orthorhombic" class="mw-redirect" title="Orthorhombic">orthorhombic</a>, it might inherently have an admixture of s-wave symmetry. So, by tuning their technique further, it was found that there was an admixture of s-wave symmetry in YBCO within about 3%.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Also, it was demonstrated by Tsuei, Kirtley et al. that there was a pure <i>d</i><sub><i>x</i><sup>2</sup>-<i>y</i><sup>2</sup></sub> order parameter symmetry in the <a href="/wiki/Tetragonal" class="mw-redirect" title="Tetragonal">tetragonal</a> Tl<sub>2</sub>Ba<sub>2</sub>CuO<sub>6</sub>.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <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=Unconventional_superconductor&action=edit&section=10" 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="CITEREFHirschMapleMarsiglio2015" class="citation journal cs1">Hirsch, J. 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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:Superconductivity" title="Template:Superconductivity"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Superconductivity" title="Template talk:Superconductivity"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Superconductivity" title="Special:EditPage/Template:Superconductivity"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Superconductivity" style="font-size:114%;margin:0 4em"><a href="/wiki/Superconductivity" title="Superconductivity">Superconductivity</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</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/BCS_theory" title="BCS theory">BCS</a></li> <li><a href="/wiki/Bean%27s_critical_state_model" title="Bean's critical state model">Bean's critical state</a></li> <li><a href="/wiki/Ginzburg%E2%80%93Landau_theory" title="Ginzburg–Landau theory">Ginzburg–Landau</a></li> <li><a href="/wiki/Kohn%E2%80%93Luttinger_superconductivity" title="Kohn–Luttinger superconductivity">Kohn–Luttinger</a></li> <li><a href="/wiki/London_equations" title="London equations">London</a></li> <li><a href="/wiki/Matthias_rules" title="Matthias rules">Matthias</a></li> <li><a href="/wiki/Mattis%E2%80%93Bardeen_theory" title="Mattis–Bardeen theory">Mattis–Bardeen</a></li> <li><a href="/wiki/Resonating_valence_bond_theory" title="Resonating valence bond theory">RVB</a></li> <li><a href="/wiki/Werthamer%E2%80%93Helfand%E2%80%93Hohenberg_theory" title="Werthamer–Helfand–Hohenberg theory">WHH</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Characteristic parameters</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/Superconducting_coherence_length" title="Superconducting coherence length">coherence length</a></li> <li><a href="/wiki/Critical_field" title="Critical field">critical field</a></li> <li><a href="/wiki/London_penetration_depth" title="London penetration depth">London penetration depth</a></li> <li><a href="/wiki/Silsbee_effect" title="Silsbee effect">Silsbee current</a></li></ul> </div></td></tr><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 href="/wiki/Abrikosov_vortex" title="Abrikosov vortex">Abrikosov vortices</a></li> <li><a href="/wiki/Andreev_reflection" title="Andreev reflection">Andreev reflection</a></li> <li><a href="/wiki/Cooper_pair" title="Cooper pair">Cooper pairs</a></li> <li><a href="/wiki/Flux_pinning" title="Flux pinning">flux pinning</a></li> <li><a href="/wiki/Flux_pumping" title="Flux pumping">flux pumping</a></li> <li><a href="/wiki/Josephson_effect" title="Josephson effect">Josephson effect</a></li> <li><a href="/wiki/Little%E2%80%93Parks_effect" title="Little–Parks effect">Little–Parks effect</a></li> <li><a href="/wiki/Meissner_effect" title="Meissner effect">Meissner effect</a></li> <li><a href="/wiki/Homes%27s_law" title="Homes's law">Homes's law</a></li> <li><a href="/wiki/Persistent_current" title="Persistent current">persistent currents</a></li> <li><a href="/wiki/Proximity_effect_(superconductivity)" title="Proximity effect (superconductivity)">proximity effect</a></li> <li><a href="/wiki/Reentrant_superconductivity" title="Reentrant superconductivity">reentrance</a></li> <li><a href="/wiki/SU(2)_color_superconductivity" title="SU(2) color superconductivity">SU(2) color</a></li> <li><a href="/wiki/Supercurrent" title="Supercurrent">supercurrents</a></li> <li><a href="/wiki/Superdiamagnetism" title="Superdiamagnetism">superdiamagnetism</a></li> <li><a href="/wiki/Superstripes" title="Superstripes">superstripes</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Superconductor_classification" title="Superconductor classification">Classification</a></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%">By magnetic response</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Types <ul><li><a href="/wiki/Type-I_superconductor" title="Type-I superconductor">I</a></li> <li><a href="/wiki/Type-II_superconductor" title="Type-II superconductor">II</a></li> <li><a href="/wiki/Type-1.5_superconductor" title="Type-1.5 superconductor">1.5</a></li></ul></li> <li><a href="/wiki/Ferromagnetic_superconductor" title="Ferromagnetic superconductor">ferromagnetic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By explanation</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/Conventional_superconductor" title="Conventional superconductor">conventional</a></li> <li><a class="mw-selflink selflink">unconventional</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By critical temperature</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>low temperature</li> <li><a href="/wiki/High-temperature_superconductivity" title="High-temperature superconductivity">high temperature</a></li> <li><a href="/wiki/Room-temperature_superconductor" title="Room-temperature superconductor">room temperature</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By composition</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/Covalent_superconductor" title="Covalent superconductor">covalent</a></li> <li><a href="/wiki/Cuprate_superconductor" title="Cuprate superconductor">cuprates</a></li> <li><a href="/wiki/Heavy_fermion_superconductor" title="Heavy fermion superconductor">heavy fermion</a></li> <li><a href="/wiki/Iron-based_superconductor" title="Iron-based superconductor">iron-based</a></li> <li><a href="/wiki/Oxypnictide" title="Oxypnictide">oxypnictides</a></li> <li><a href="/wiki/Organic_superconductor" title="Organic superconductor">organic</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Technological_applications_of_superconductivity" title="Technological applications of superconductivity">Technological applications</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/Cryotron" title="Cryotron">cryotron</a></li> <li><a href="/wiki/Superconducting_magnet" title="Superconducting magnet">electromagnets</a></li> <li><a href="/wiki/Magnetic_resonance_imaging" title="Magnetic resonance imaging">MRI</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">NMR</a></li> <li><a href="/wiki/Superconducting_quantum_computing" title="Superconducting quantum computing">quantum computing</a></li> <li><a href="/wiki/Rutherford_cable" title="Rutherford cable">Rutherford cable</a></li> <li><a href="/wiki/SQUID" title="SQUID">SQUID</a></li> <li><a href="/wiki/Superconducting_wire" title="Superconducting wire">wires</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">List of superconductors</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/Bilayer_graphene" title="Bilayer graphene">bilayer graphene</a></li> <li><a href="/wiki/BSCCO" class="mw-redirect" title="BSCCO">BSCCO</a></li> <li><a href="/wiki/Lanthanum_barium_copper_oxide" title="Lanthanum barium copper oxide">LBCO</a></li> <li><a href="/wiki/Magnesium_diboride" title="Magnesium diboride">MgB<sub>2</sub></a></li> <li><a href="/wiki/Niobium%E2%80%93tin" title="Niobium–tin">NbSn</a></li> <li><a href="/wiki/Niobium%E2%80%93titanium" title="Niobium–titanium">NbTi</a></li> <li><a href="/wiki/Thallium_barium_calcium_copper_oxide" title="Thallium barium calcium copper oxide">TBCCO</a></li> <li><a href="/wiki/YBCO" class="mw-redirect" title="YBCO">YBCO</a></li> <li><a href="/wiki/List_of_superconductors" title="List of superconductors">more...</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img 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