Correlation-Induced Insulating Topological Phases at Charge Neutrality in Twisted Bilayer Graphene

Yuan Da Liao, Jian Kang, Clara N. Breiø, Xiao Yan Xu, Han Qing Wu, Brian M. Andersen, Rafael M. Fernandes, Zi Yang Meng

Research output: Contribution to journalArticlepeer-review

Abstract

Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom - charge, spin, and valley - gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

Original languageEnglish (US)
Article number011014
JournalPhysical Review X
Volume11
Issue number1
DOIs
StatePublished - Jan 22 2021

Bibliographical note

Funding Information:
We thank Eslam Khalaf, Ashvin Vishwanath, and Yi Zhang for insightful conversations on the subject, especially on the nature of the IVC phase. We also thank Oskar Vafek for valuable suggestions and for pointing out a missing factor in the IVC correlation function. Y. D. L. and Z. Y. M. acknowledge support from the National Key Research and Development Program of China (Grant No. 2016YFA0300502) and Research Grants Council of Hong Kong SAR China (Grant No. 17303019). H. Q. W. is supported by NSFC through Grant No. 11804401 and the Fundamental Research Funds for the Central Universities. J. K. acknowledges support from the NSFC Grant No. 12074276, and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions. R. M. F. is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0020045. Y. D. L. and Z. Y. M. thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science and Information Technology Service at the University of Hong Kong, the Platform for Data-Driven Computational Materials Discovery at the Songshan Lake Materials Laboratory and the National Supercomputer Centers in Tianjin and Guangzhou for their technical support and generous allocation of CPU time. J. K. thanks the Kavli Institute for Theoretical Sciences for hospitality during the completion of this work. Z. Y. M., J. K., and R. M. F. acknowledge the hospitality of the Aspen Center for Physics, where part of this work was developed. The Aspen Center for Physics is supported by National Science Foundation Grant No. PHY-1607611.

Funding Information:
We thank Eslam Khalaf, Ashvin Vishwanath, and Yi Zhang for insightful conversations on the subject, especially on the nature of the IVC phase. We also thank Oskar Vafek for valuable suggestions and for pointing out a missing factor in the IVC correlation function. Y. D. L. and Z. Y. M. acknowledge support from the National Key Research and Development Program of China (Grant No. 2016YFA0300502) and Research Grants Council of Hong Kong SAR China (Grant No. 17303019). H. Q. W. is supported by NSFC through Grant No. 11804401 and the Fundamental Research Funds for the Central Universities. J. K. acknowledges support from the NSFC Grant No. 12074276, and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions. R. M. F. is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award No. DE-SC0020045. Y. D. L. and Z. Y. M. thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science and Information Technology Service at the University of Hong Kong, the Platform for Data-Driven Computational Materials Discovery at the Songshan Lake Materials Laboratory and the National Supercomputer Centers in Tianjin and Guangzhou for their technical support and generous allocation of CPU time. J. K. thanks the Kavli Institute for Theoretical Sciences for hospitality during the completion of this work. Z. Y. M., J. K., and R. M. F. acknowledge the hospitality of the Aspen Center for Physics, where part of this work was developed. The Aspen Center for Physics is supported by National Science Foundation Grant No. PHY-1607611.

Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

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