双层石墨烯最低朗道水平相变的红外光谱学

IF 8.1 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
B. Jordan Russell, Matheus Schossler, Jesse Balgley, Yashika Kapoor, T. Taniguchi, K. Watanabe, Alexander Seidel, Yafis Barlas, Erik A. Henriksen
{"title":"双层石墨烯最低朗道水平相变的红外光谱学","authors":"B. Jordan Russell, Matheus Schossler, Jesse Balgley, Yashika Kapoor, T. Taniguchi, K. Watanabe, Alexander Seidel, Yafis Barlas, Erik A. Henriksen","doi":"10.1103/physrevlett.133.196402","DOIUrl":null,"url":null,"abstract":"We perform infrared magnetospectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At <mjx-container ctxtmenu_counter=\"37\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(3 0 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"nu equals 4\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>4</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At <mjx-container ctxtmenu_counter=\"38\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"nu equals 0\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container> when the octet is half-filled, multiple resonances disperse nonmonotonically with increasing displacement field, <mjx-container ctxtmenu_counter=\"39\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper D\" data-semantic-type=\"identifier\"><mjx-c>𝐷</mjx-c></mjx-mi></mjx-math></mjx-container>, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted antiferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in <mjx-container ctxtmenu_counter=\"40\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper D\" data-semantic-type=\"identifier\"><mjx-c>𝐷</mjx-c></mjx-mi></mjx-math></mjx-container>. When <mjx-container ctxtmenu_counter=\"41\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"upper D equals 0\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐷</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container> and <mjx-container ctxtmenu_counter=\"42\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"greekletter\" data-semantic-speech=\"nu\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi></mjx-math></mjx-container> is varied, resonances at <mjx-container ctxtmenu_counter=\"43\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"addition\" data-semantic-speech=\"plus or minus nu\" data-semantic-structure=\"(2 0 1)\" data-semantic-type=\"prefixop\"><mjx-mo data-semantic- data-semantic-operator=\"prefixop,±\" data-semantic-parent=\"2\" data-semantic-role=\"addition\" data-semantic-type=\"operator\"><mjx-c>±</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi></mjx-math></mjx-container> show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The <mjx-container ctxtmenu_counter=\"44\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"nu equals 4\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>4</mjx-c></mjx-mn></mjx-math></mjx-container> data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However, even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at <mjx-container ctxtmenu_counter=\"45\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"nu equals 0\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container>. Our results suggest additional physics is required to understand bilayer graphene at half-filling.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":"147 1","pages":""},"PeriodicalIF":8.1000,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Infrared Spectroscopy of Phase Transitions in the Lowest Landau Levels of Bilayer Graphene\",\"authors\":\"B. Jordan Russell, Matheus Schossler, Jesse Balgley, Yashika Kapoor, T. Taniguchi, K. Watanabe, Alexander Seidel, Yafis Barlas, Erik A. Henriksen\",\"doi\":\"10.1103/physrevlett.133.196402\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We perform infrared magnetospectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At <mjx-container ctxtmenu_counter=\\\"37\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(3 0 1 2)\\\"><mjx-mrow data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"nu equals 4\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\" space=\\\"4\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>4</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At <mjx-container ctxtmenu_counter=\\\"38\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"nu equals 0\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container> when the octet is half-filled, multiple resonances disperse nonmonotonically with increasing displacement field, <mjx-container ctxtmenu_counter=\\\"39\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"0\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"upper D\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐷</mjx-c></mjx-mi></mjx-math></mjx-container>, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted antiferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in <mjx-container ctxtmenu_counter=\\\"40\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"0\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"upper D\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐷</mjx-c></mjx-mi></mjx-math></mjx-container>. When <mjx-container ctxtmenu_counter=\\\"41\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"upper D equals 0\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐷</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container> and <mjx-container ctxtmenu_counter=\\\"42\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"0\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-role=\\\"greekletter\\\" data-semantic-speech=\\\"nu\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi></mjx-math></mjx-container> is varied, resonances at <mjx-container ctxtmenu_counter=\\\"43\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-children=\\\"1\\\" data-semantic-content=\\\"0\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-role=\\\"addition\\\" data-semantic-speech=\\\"plus or minus nu\\\" data-semantic-structure=\\\"(2 0 1)\\\" data-semantic-type=\\\"prefixop\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"prefixop,±\\\" data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"addition\\\" data-semantic-type=\\\"operator\\\"><mjx-c>±</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi></mjx-math></mjx-container> show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The <mjx-container ctxtmenu_counter=\\\"44\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"nu equals 4\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>4</mjx-c></mjx-mn></mjx-math></mjx-container> data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However, even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at <mjx-container ctxtmenu_counter=\\\"45\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"nu equals 0\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"greekletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>0</mjx-c></mjx-mn></mjx-math></mjx-container>. Our results suggest additional physics is required to understand bilayer graphene at half-filling.\",\"PeriodicalId\":20069,\"journal\":{\"name\":\"Physical review letters\",\"volume\":\"147 1\",\"pages\":\"\"},\"PeriodicalIF\":8.1000,\"publicationDate\":\"2024-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical review letters\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevlett.133.196402\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevlett.133.196402","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

我们对双栅双层石墨烯中的朗道水平(LL)跃迁进行了红外磁谱分析。在 𝜈=4 时,当第四个 LL(八位位组)被填满时,观察到两个共振,表明间隙被打开。在 𝜈=0 时,当八元组填充一半时,多个共振随着垂直于薄片的位移场 𝐷 的增加而非单调地分散,显示出在适度位移场下从倾斜反铁磁体 (CAFM) 向层极化态的相变,间隙随 𝐷 的增加而线性打开。当 𝐷=0 和 𝜈 变化时,±𝜈 处的共振显示出电子-空穴的不对称性,随着八元组的逐渐填充,会出现多线分裂。当考虑到双层石墨烯四带模型中的多个紧密结合项时,𝜈=4 的数据与平均场 Hartree-Fock 计算的预测结果非常一致。我们的结果表明,要理解半填充状态下的双层石墨烯,还需要更多的物理知识。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Infrared Spectroscopy of Phase Transitions in the Lowest Landau Levels of Bilayer Graphene
We perform infrared magnetospectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At 𝜈=4 when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At 𝜈=0 when the octet is half-filled, multiple resonances disperse nonmonotonically with increasing displacement field, 𝐷, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted antiferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in 𝐷. When 𝐷=0 and 𝜈 is varied, resonances at ±𝜈 show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The 𝜈=4 data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However, even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at 𝜈=0. Our results suggest additional physics is required to understand bilayer graphene at half-filling.
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来源期刊
Physical review letters
Physical review letters 物理-物理:综合
CiteScore
16.50
自引率
7.00%
发文量
2673
审稿时长
2.2 months
期刊介绍: Physical review letters(PRL)covers the full range of applied, fundamental, and interdisciplinary physics research topics: General physics, including statistical and quantum mechanics and quantum information Gravitation, astrophysics, and cosmology Elementary particles and fields Nuclear physics Atomic, molecular, and optical physics Nonlinear dynamics, fluid dynamics, and classical optics Plasma and beam physics Condensed matter and materials physics Polymers, soft matter, biological, climate and interdisciplinary physics, including networks
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