Faithful tight-binding models and fragile topology of magic-angle bilayer graphene

被引:316
作者
Po, Hoi Chun [1 ,2 ]
Zou, Liujun [1 ,2 ]
Senthil, T. [2 ]
Vishwanath, Ashvin [1 ]
机构
[1] Harvard Univ, Dept Phys, Cambridge, MA 02138 USA
[2] MIT, Dept Phys, Cambridge, MA 02139 USA
基金
美国国家科学基金会;
关键词
MOIRE BANDS; INSULATOR; ELECTRONS;
D O I
10.1103/PhysRevB.99.195455
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Correlated insulators and superconductivity have been observed in "magic-angle" twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the "fragile topology" of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model.
引用
收藏
页数:16
相关论文
共 62 条
[41]   Fragile Topology and Wannier Obstructions [J].
Po, Hoi Chun ;
Watanabe, Haruki ;
Vishwanath, Ashvin .
PHYSICAL REVIEW LETTERS, 2018, 121 (12)
[42]  
Po HC, 2017, NAT COMMUN, V8, DOI 10.1038/s41467-017-00133-2
[43]   Filling-enforced quantum band insulators in spin-orbit coupled crystals [J].
Po, Hoi Chun ;
Watanabe, Haruki ;
Zaletel, Michael P. ;
Vishwanath, Ashvin .
SCIENCE ADVANCES, 2016, 2 (04)
[44]   Generic Wave-Function Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators [J].
Qi, Xiao-Liang .
PHYSICAL REVIEW LETTERS, 2011, 107 (12)
[45]   Charge-transfer insulation in twisted bilayer graphene [J].
Rademaker, Louk ;
Mellado, Paula .
PHYSICAL REVIEW B, 2018, 98 (23)
[46]   Electrically Tunable Gauge Fields in Tiny-Angle Twisted Bilayer Graphene [J].
Ramires, Aline ;
Lado, Jose L. .
PHYSICAL REVIEW LETTERS, 2018, 121 (14)
[47]   Transport Through a Network of Topological Channels in Twisted Bilayer Graphene [J].
Rickhaus, Peter ;
Wallbank, John ;
Slizovskiy, Sergey ;
Pisoni, Riccardo ;
Overweg, Hiske ;
Lee, Yongjin ;
Eich, Marius ;
Liu, Ming-Hao ;
Watanabe, Kenji ;
Taniguchi, Takashi ;
Ihn, Thomas ;
Ensslin, Klaus .
NANO LETTERS, 2018, 18 (11) :6725-6730
[48]   Electronic spectrum of twisted bilayer graphene [J].
Sboychakov, A. O. ;
Rakhmanov, A. L. ;
Rozhkov, A. V. ;
Nori, Franco .
PHYSICAL REVIEW B, 2015, 92 (07)
[49]   Electronic structure of turbostratic graphene [J].
Shallcross, S. ;
Sharma, S. ;
Kandelaki, E. ;
Pankratov, O. A. .
PHYSICAL REVIEW B, 2010, 81 (16)
[50]   Wannier representation of Z2 topological insulators [J].
Soluyanov, Alexey A. ;
Vanderbilt, David .
PHYSICAL REVIEW B, 2011, 83 (03)