Shaping the topology of twisted bilayer graphene via time-reversal symmetry breaking

TL;DR

This paper explores how breaking time-reversal symmetry in twisted bilayer graphene induces a topological phase transition, revealing new insulating states and measurable anomalous Hall effects driven by Berry curvature.

Contribution

It demonstrates a controllable topological phase transition in TBG via TRSB, including the characterization of a novel insulating phase with zero Chern number but non-zero Berry curvature effects.

Findings

Identification of a topological phase transition mediated by gap closing at the $b3$ point.

Construction of a three-dimensional phase diagram involving twisting angle, symmetry-breaking strength, and stacking mismatch.

Proposal to detect the new phase through non-quantized anomalous Hall conductivity measurements.

Abstract

Symmetry breaking is an effective tool for tuning the transport and topological properties of 2D layered materials. Among these materials, twisted bilayer graphene (TBG) has emerged as a promising platform for new physics, characterized by a rich interplay between topological features and strongly correlated electronic behavior. In this study, we utilize time-reversal symmetry breaking (TRSB) to manipulate the topological properties of TBG. By varying the strength of TRSB, we discover a topological phase transition between a topological insulating phase, which exhibits a pair of flat bands with opposite Chern numbers, and a novel insulating state where the Chern number, but not the Berry curvature, of the flat bands vanishes. We demonstrate that this topological transition is mediated by a gap closing at the $\Gamma$ point, and we construct a three-dimensional phase diagram as a function of the twisting angle, the symmetry-breaking parameter, and the mismatch coupling between AA and AB stacking regions. Finally, we show that this novel electronic phase can be identified in the lab by measuring, as a function of the Fermi energy, its non-quantized anomalous Hall conductivity that is induced by the Berry dipole density of the lowest flat bands.