{"title":"扭曲双层石墨烯中的相关切尔绝缘体理论","authors":"Xiaoyu Wang, Oskar Vafek","doi":"10.1103/physrevx.14.021042","DOIUrl":null,"url":null,"abstract":"Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi></math> at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math> for <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo>±</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>4</mn><mo stretchy=\"false\">)</mo></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy=\"false\">)</mo></math>, and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math>. We also find correlated Chern insulators at unconventional sequences with <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi><mo>+</mo><mi>t</mi><mo>≠</mo><mo>±</mo><mn>4</mn></math>, as well as with fractional <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi></math>, and elucidate their nature.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":11.6000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Theory of Correlated Chern Insulators in Twisted Bilayer Graphene\",\"authors\":\"Xiaoyu Wang, Oskar Vafek\",\"doi\":\"10.1103/physrevx.14.021042\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>s</mi></math> at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>t</mi></math> for <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo stretchy=\\\"false\\\">(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo stretchy=\\\"false\\\">)</mo><mo>=</mo><mo>±</mo><mo stretchy=\\\"false\\\">(</mo><mn>0</mn><mo>,</mo><mn>4</mn><mo stretchy=\\\"false\\\">)</mo></math>, <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>±</mo><mo stretchy=\\\"false\\\">(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo stretchy=\\\"false\\\">)</mo></math>, <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>±</mo><mo stretchy=\\\"false\\\">(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy=\\\"false\\\">)</mo></math>, and <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo>±</mo><mo stretchy=\\\"false\\\">(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo stretchy=\\\"false\\\">)</mo></math>. 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引用次数: 0
摘要
魔角扭曲双层石墨烯是研究得最透彻的物理平台,其特点是摩尔势诱导的窄带具有非难拓扑和强电子相关性。尽管其重要性不言而喻,但在有限磁场下观察到的切尔诺绝缘态--推断为零磁场下的带填充态--仍然鲜为人知。揭示其本质是摩尔材料领域最重要的未决问题之一。在此,我们首次对有限磁场中的相互作用电子进行了全面研究,同时改变了电子密度、扭转角和异应变。在扭转角范围内出现的一系列相关切尔恩相中,我们发现了一个统一的描述,即在(s,t)=±(0,4)、±(1,3)、±(2,2)和±(3,1)时,切尔恩数为 t 的无处不在的状态序列。我们还在 s+t≠±4 以及分数 s 的非常规序列中发现了相关的切尔诺绝缘体,并阐明了它们的性质。
Theory of Correlated Chern Insulators in Twisted Bilayer Graphene
Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number for , , , and . We also find correlated Chern insulators at unconventional sequences with , as well as with fractional , and elucidate their nature.
期刊介绍:
Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.