Realization of topological Mott insulator in a twisted bilayer graphene lattice model

Bin-Bin Chen,Jian Kang,Wei Li,Ziyu Chen,Zi Yang Meng,Yuan Da Liao,Oskar Vafek

doi:10.1038/s41467-021-25438-1

Abstract

Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.

Highlights

Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands
There exists no a priori Wannier obstruction, as the narrow bands’ total Chern number vanishes, there is yet no clear understanding of how the quantum anomalous Hall (QAH) could arise within such correlated lattice model, even in principle, in the limit where the Coulomb interactions dominate the kinetic energy
For a typical QAH state with α = 0.25, we show in d the charge density nλ(k), with λ labeling the two eigenvalues of the 2 × 2G~ðkÞ matrix associated with two sublattices

Summary

Introduction

Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. There exists no a priori Wannier obstruction, as the narrow bands’ total Chern number vanishes, there is yet no clear understanding of how the QAH could arise within such correlated lattice model, even in principle, in the limit where the Coulomb interactions dominate the kinetic energy. Such a state was sought by Raghu et al in an entirely different context[47], coining the term topological Mott insulator (TMI), which we define to be a QAH in a strong coupling limit of a local lattice model with a vanishing ratio of the bandwidth to Coulomb interaction. More recent works have found the interactioninduced QAH state in a different model, but it is stabilized by the kinetic energy and necessitates sizable bandwidth[50,51,52]

Methods

Results

Conclusion