Dirac point movement and topological phase transition in patterned graphene

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If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semicondu" /> <link rel="canonical" href="https://pubs.rsc.org/en/content/articlelanding/2015/nr/c4nr06454b" /> <meta name="DC.Creator" content="Marc Dvorak" /> <meta content="Marc Dvorak" name="citation_author" /><meta content="Department of Physics, Colorado School of Mines, Golden, CO, USA" name="citation_author_institution" /> <meta name="DC.Creator" content="Zhigang Wu" /> <meta content="Zhigang Wu" name="citation_author" /><meta content="Department of Physics, Colorado School of Mines, Golden, CO, USA" name="citation_author_institution" /><meta name="DC.title" content="Dirac point movement and topological phase transition in patterned graphene" /> <meta name="DC.publisher" content="The Royal Society of Chemistry" /> <meta name="DC.issued" content="2015/01/26" /> <meta name="DC.Identifier" content="10.1039/C4NR06454B" /> <meta name="DC.Language" content="en" /> <meta name="PPL.DocType" content="journals" /> <meta name="description" content="The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. 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Matter; citation_volume=14; citation_pages=2745;citation_publication_date=2002; " /> <meta name="citation_reference" content="citation_author=G. Kresse; citation_author=J. Furthmüller; citation_journal_title=Phys. Rev. B: Condens. Matter; citation_volume=54; citation_pages=11169-11186;citation_publication_date=1996; " /> <meta name="citation_reference" content="citation_author=J. P. Perdew; citation_author=K. Burke; citation_author=M. Ernzerhof; citation_journal_title=Phys. Rev. Lett.; citation_volume=77; citation_pages=3865-3868;citation_publication_date=1996; " /> <meta content=" The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition. 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Click to view all articles in this issue." title="Issue 8, 2015">Issue 8, 2015</a> </div> <nav aria-label="Article"> <ul class="article-nav__bar"> <li> <a href="/en/Content/ArticleLanding/2015/NR/C4NR06755J"> Previous <span class="v-mobile-hide--inline">Article</span> </a> </li> <li> <a href="/en/Content/ArticleLanding/2015/NR/C4NR07078J"> Next <span class="v-mobile-hide--inline">Article</span> </a> </li> </ul> </nav> <div class="list-control"> <div class="list__collection--image"> <div class="list__item"> <a href="/en/journals/journal/nr" class="list__item-link"> <div class="list__image-col"> <img src="/en/Image/Get?imageInfo.ImageType=CoverIssue&imageInfo.ImageIdentifier.SerCode=NR&imageInfo.ImageIdentifier.IssueId=NR007008" id="imgLoader" alt="" class="list__item-img" height="88"> </div> <div class="list__text-col"> <div class="list__item-label"> <span class="page-head__context">From the journal:</span> <h3 class="h--heading3 no-heading">Nanoscale</h3> </div> </div> </a> </div> </div> </div> <br> </div> <article class="article-control"> <div class="article__title"> <h2 class="capsule__title fixpadv--m"> Dirac point movement and topological phase transition in patterned graphene<a href="#fn1" title="Electronic supplementary information (ESI) available. See DOI: 10.1039/c4nr06454b">†</a> </h2> <div class="fixpadv--m crossmark-button"> <button type="button" data-target="crossmark"><img width="150" height="32" src="https://crossmark-cdn.crossref.org/widget/v2.0/logos/CROSSMARK_Color_horizontal.svg" alt="Check for updates" /></button> </div> </div> <div class="article__authors"> <span class="article__author-link"> <a href="/en/results?searchtext=Author%3AMarc%20Dvorak">Marc Dvorak</a><span><sup><i>a</i></sup></span>  and  </span> <span class="article__author-link"> <a href="/en/results?searchtext=Author%3AZhigang%20Wu">Zhigang Wu</a>*<span><sup><i>a</i></sup></span>   </span> </div> <div class="drawer-control fixpadv--m"> <a href="#" role="button" id="btnAuthorAffiliations" aria-expanded="false" aria-controls="pnlAuthorAffiliations" class="drawer__handle"> <span class="drawer__icon"></span> Author affiliations </a> <div class="drawer__content" id="pnlAuthorAffiliations" aria-labelledby="btnAuthorAffiliations"> <div> <p class="article__author-affiliation"> <span> * </span> <span> Corresponding authors </span> </p> <p class="article__author-affiliation"> <span> <sup>a</sup> </span> <span> Department of Physics, Colorado School of Mines, Golden, CO, USA <br /> <b>E-mail:</b> <a href="mailto:zhiwu@mines.edu" title="zhiwu@mines.edu">zhiwu@mines.edu</a> </span> </p> </div> </div> </div> <h3 class="h--heading3 article-abstract__heading">Abstract</h3> <div class="capsule__column-wrapper"> <div class="capsule__text"> <p xmlns="http://www.rsc.org/schema/rscart38">The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the <em>C</em><small><sub>3</sub></small> symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.</p> </div> <div class="capsule__article-image fixpadv--s"> <img src="/en/Image/Get?imageInfo.ImageType=GA&imageInfo.ImageIdentifier.ManuscriptID=C4NR06454B&imageInfo.ImageIdentifier.Year=2015" alt="Graphical abstract: Dirac point movement and topological phase transition in patterned graphene" /> </div> </div> <p></p> <div id="pnlArticleAccess" class="article-access fixpadt--xxl" style="display: none; border: 0;"> <div class="article-access__inner" style="background-color: #F1F1F3;"> <div class="article-access__head fixpad--s"> You have access to this article </div> <div class="fixpad--xl"> <div id="pnlViewFullArticleButton" class="paywall__body text--centered"> <div id="pnlArticleLoading"> <span id="thtmlLoadingMessage"> <img src="https://www.rsc-cdn.org/pubs-core/2022.0.159/content/NewImages/Ajax-GA-Loader.gif" alt="" 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Dirac point movement and topological phase transition in patterned graphene - Nanoscale (RSC Publishing)