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{"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}
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