具有隐藏拓扑相的α-锑烯中的高自旋-切尔数绝缘体

IF 4.5 3区 材料科学 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY
Baokai Wang, Xiaoting Zhou, Yi-Chun Hung, Yen-Chuan Lin, Hsin Lin, Arun Bansil
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The spin Chern number <inline-formula>\n<tex-math><?CDATA $\\mathcal{C}_s$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"tdmad3136ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> is presumed to yield the same topological classification as the <inline-formula>\n<tex-math><?CDATA $\\mathbb{Z}_2$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"tdmad3136ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> invariant. Here, by investigating the electronic structures of monolayer <italic toggle=\"yes\">α</italic>-phase group V elements, we uncover the presence of a topological phase in <italic toggle=\"yes\">α</italic>-Sb, which can be characterized by a spin Chern number <inline-formula>\n<tex-math><?CDATA $\\mathcal{C}_s$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"tdmad3136ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> = 2, even though it is <inline-formula>\n<tex-math><?CDATA $\\mathbb{Z}_2$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"tdmad3136ieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> trivial. Although <italic toggle=\"yes\">α</italic>-As and Sb would thus be classified as trivial insulators within the classification schemes, we demonstrate the existence of a phase transition between <italic toggle=\"yes\">α</italic>-As and Sb, which is induced by band inversions at two generic <italic toggle=\"yes\">k</italic> points. Without spin–orbit coupling (SOC), <italic toggle=\"yes\">α</italic>-As is a trivial insulator, while <italic toggle=\"yes\">α</italic>-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the DPs and induces a nontrivial Berry curvature, endowing <italic toggle=\"yes\">α</italic>-Sb with a high spin Chern number of <inline-formula>\n<tex-math><?CDATA $\\mathcal{C}_s$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"tdmad3136ieqn6.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> = 2. We further show that monolayer <italic toggle=\"yes\">α</italic>-Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges, as expected from topological considerations.","PeriodicalId":6812,"journal":{"name":"2D Materials","volume":"5 1","pages":""},"PeriodicalIF":4.5000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"High spin-Chern-number insulator in α-antimonene with a hidden topological phase\",\"authors\":\"Baokai Wang, Xiaoting Zhou, Yi-Chun Hung, Yen-Chuan Lin, Hsin Lin, Arun Bansil\",\"doi\":\"10.1088/2053-1583/ad3136\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the <inline-formula>\\n<tex-math><?CDATA $\\\\mathbb{Z}_2$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"tdmad3136ieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> topological insulator phase in the existing literature. The spin Chern number <inline-formula>\\n<tex-math><?CDATA $\\\\mathcal{C}_s$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"tdmad3136ieqn2.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> is presumed to yield the same topological classification as the <inline-formula>\\n<tex-math><?CDATA $\\\\mathbb{Z}_2$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\\\"double-struck\\\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"tdmad3136ieqn3.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> invariant. 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Although <italic toggle=\\\"yes\\\">α</italic>-As and Sb would thus be classified as trivial insulators within the classification schemes, we demonstrate the existence of a phase transition between <italic toggle=\\\"yes\\\">α</italic>-As and Sb, which is induced by band inversions at two generic <italic toggle=\\\"yes\\\">k</italic> points. Without spin–orbit coupling (SOC), <italic toggle=\\\"yes\\\">α</italic>-As is a trivial insulator, while <italic toggle=\\\"yes\\\">α</italic>-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the DPs and induces a nontrivial Berry curvature, endowing <italic toggle=\\\"yes\\\">α</italic>-Sb with a high spin Chern number of <inline-formula>\\n<tex-math><?CDATA $\\\\mathcal{C}_s$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"tdmad3136ieqn6.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> = 2. 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引用次数: 0

摘要

对于时间反转对称系统,量子自旋霍尔相假设与现有文献中的 Z2 拓扑绝缘体相相同。自旋切尔诺数 Cs 被假定为产生与 Z2 不变量相同的拓扑分类。在这里,我们通过研究单层α相 V 族元素的电子结构,发现了α-Sb 中存在拓扑相,它可以用自旋切尔数 Cs = 2 来表征,尽管它是 Z2 三相。虽然 α-As 和 Sb 在分类方案中被归类为微不足道的绝缘体,但我们证明了 α-As 和 Sb 之间存在相变,这种相变是由两个通用 k 点的带反转引起的。在没有自旋轨道耦合(SOC)的情况下,α-As 是一个微不足道的绝缘体,而 α-Sb 则是一个具有四个远离高对称性线的狄拉克点(DP)的狄拉克半金属。加入 SOC 后,DP 会出现间隙,并产生非微不足道的贝里曲率,从而赋予 α-Sb Cs = 2 的高自旋切尔数。我们进一步证明,单层 α-Sb 表现出无间隙带状结构或其边缘的无间隙自旋谱,这是拓扑学所预期的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
High spin-Chern-number insulator in α-antimonene with a hidden topological phase
For a time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the Z2 topological insulator phase in the existing literature. The spin Chern number Cs is presumed to yield the same topological classification as the Z2 invariant. Here, by investigating the electronic structures of monolayer α-phase group V elements, we uncover the presence of a topological phase in α-Sb, which can be characterized by a spin Chern number Cs = 2, even though it is Z2 trivial. Although α-As and Sb would thus be classified as trivial insulators within the classification schemes, we demonstrate the existence of a phase transition between α-As and Sb, which is induced by band inversions at two generic k points. Without spin–orbit coupling (SOC), α-As is a trivial insulator, while α-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the DPs and induces a nontrivial Berry curvature, endowing α-Sb with a high spin Chern number of Cs = 2. We further show that monolayer α-Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges, as expected from topological considerations.
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来源期刊
2D Materials
2D Materials MATERIALS SCIENCE, MULTIDISCIPLINARY-
CiteScore
10.70
自引率
5.50%
发文量
138
审稿时长
1.5 months
期刊介绍: 2D Materials is a multidisciplinary, electronic-only journal devoted to publishing fundamental and applied research of the highest quality and impact covering all aspects of graphene and related two-dimensional materials.
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