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Chin. Phys. B, 2021, Vol. 30(1): 017305    DOI: 10.1088/1674-1056/abcfa3
Special Issue: SPECIAL TOPIC —Twistronics
TOPICAL REVIEW—Twistronics Prev   Next  

Correlated insulating phases in the twisted bilayer graphene

Yuan-Da Liao(廖元达)1,2, Xiao-Yan Xu(许霄琰)3, Zi-Yang Meng(孟子杨)4,1,5,†, and Jian Kang(康健)6,
1 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; 2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; 3 Department of Physics, University of California at San Diego, La Jolla, California 92093, USA; 4 Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China; 5 Songshan Lake Materials Laboratory, Dongguan 523808, China; 6 School of Physical Science and Technology & Institute for Advanced Study, Soochow University, Suzhou 215006, China
Abstract  We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is SU(4) symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the SU(4) manifold with degeneracy. The kinetic terms, treated as perturbation, break this large SU(4) symmetry and propel the appearance of intervalley coherent state, quantum topological insulators, and other symmetry-breaking insulating states. We first present the theoretical analysis of moir\'e lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.
Keywords:  twisted bilayer graphene      correlated insulator      quantum Monte Carlo simulation  
Revised:  18 November 2020      Published:  30 December 2020
PACS:  73.22.Pr (Electronic structure of graphene)  
  73.21.Cd (Superlattices)  
  73.22.Gk (Broken symmetry phases)  
Fund: YDL and ZYM acknowledge support from the National Key Research and Development Program of China (Grant No. 2016YFA0300502) and the Research Grants Council of Hong Kong SAR China (Grant Nos. 17303019 and 17301420). JK is supported by Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions, China.
Corresponding Authors:  Corresponding author. E-mail: zymeng@hku.hk Corresponding author. E-mail: jkang@suda.edu.cn   

Cite this article: 

Yuan-Da Liao(廖元达), Xiao-Yan Xu(许霄琰), Zi-Yang Meng(孟子杨), and Jian Kang(康健) Correlated insulating phases in the twisted bilayer graphene 2021 Chin. Phys. B 30 017305

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