Topological phase transition from trigonal warping in van der Waals multilayers

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, such as 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 a large exchange field and/or interlayer potential difference by inducing extra band inversion points at a momentum further away from the high-symmetry point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of a valley-polarized QAHE with high Chern numbers ranging from $\mathcal{C}=\ensuremath{-}7$ to 7 . These results suggest that the universal trigonal warping may play an important role when the Bloch states at momenta deviated from high-symmetry points are involved.