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

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78 Scopus citations

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

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

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