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 2D Materials Pub Date : 2024-03-26 DOI:10.1088/2053-1583/ad3136
Baokai Wang, Xiaoting Zhou, Yi-Chun Hung, Yen-Chuan Lin, Hsin Lin, Arun Bansil
{"title":"具有隐藏拓扑相的α-锑烯中的高自旋-切尔数绝缘体","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. 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. 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\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2D Materials\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1088/2053-1583/ad3136\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2D Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1088/2053-1583/ad3136","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
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。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
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.
期刊最新文献
Constructing three-dimensional GO/CNT@NMP aerogels towards primary lithium metal batteries Two-dimensional Janus MXTe (M = Hf, Zr; X = S, Se) piezoelectrocatalysts: a comprehensive investigation of its electronic, synthesis feasibility, electric polarization, and hydrogen evolution reaction activity The future of Xenes beyond graphene: challenges and perspective Soft-carbon-tuned hard carbon anode for ultrahigh-rate sodium storage Multiscale computational modeling techniques in study and design of 2D materials: recent advances, challenges, and opportunities
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1