Topological phase transition from trigonal warping in van der Waals multilayers

TL;DR

This paper explores how trigonal warping influences topological phases in van der Waals multilayers, revealing its crucial role in inducing and modifying quantum anomalous Hall and valley Hall effects, especially in bilayer graphene.

Contribution

It demonstrates that trigonal warping significantly affects topological phase formation, leading to valley-polarized QAHE with high Chern numbers in bilayer graphene.

Findings

Trigonal warping induces extra band inversion points.

It shrinks the phase space of QAHE and QVHE.

Valley-polarized QAHE with Chern numbers from -7 to 7 emerges.

Abstract

In van der Waals multilayers of triangular lattice, trigonal warping occurs universally due to the interlayer hopping. We theoretically investigate the effect of trigonal warping upon distinctive topological phases, like the quantum anomalous Hall effect (QAHE) and the quantum valley Hall effect (QVHE). Taking Bernal-stacked bilayer graphene as an example, we find that the trigonal warping plays a crucial role in the formation of QAHE in large exchange field and/or interlayer potential difference by inducing extra band inversion points at momentum further away from high symmetric point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of valley-polarized QAHE with high Chern numbers ranging from $ \mathcal{C}=-7 $ to $ 7 $. These results suggest that the universal trigonal warping may play important role when the Bloch states at momentum away from high-symmetric points are involved.