Topological phase transitions in twisted bilayer graphene/hBN from interlayer coupling and substrate potentials

TL;DR

This study systematically explores topological phase transitions in twisted bilayer graphene aligned with hBN, revealing how interlayer coupling and substrate potentials induce diverse topological states and band-inversion mechanisms.

Contribution

It provides a comprehensive phase diagram of topological states in TBG/hBN, highlighting the influence of material parameters on topological transitions and Chern numbers.

Findings

Mapping of Chern number phase diagrams across parameter space.

Identification of high-Chern number states (C=3,4,5).

Linking topological transitions to band-inversion mechanisms.

Abstract

Twisted bilayer graphene aligned with hexagonal boron nitride (TBG/hBN) hosts rich topological and correlated quantum phases, such as (fractional) Chern insulators, whose character is dictated by the topology of the moir\'{e} flat band. This topology is highly sensitive to several material parameters in the continuum model, yet a systematic understanding of their combined influence has been lacking. Here, we present a comprehensive study of topological phase transitions in TBG/hBN by varying the interlayer hopping strengths ($w_0, w_1$) and hBN-induced staggered potential, both with and without the hBN moir\'{e} potential. We map out Chern number phase diagrams across a broad, experimentally relevant parameter space, revealing a progressive enrichment of the topological landscape including multiple high-Chern number ($C$ = 3, 4, and 5) states. Each transition is linked to distinct band-inversion mechanisms at generic $C_3$-symmetric k points, high-symmetry momenta, or parabolic touchings, clearly reflecting in the evolution of the Berry curvature. Our results offer theoretical insights that help interpret existing experimental observations, elucidate the mechanisms driving these topological phase transitions and facilitate the exploration of topological states in TBG/hBN and related moir\'{e} systems.