▎ 摘　　要

We study the tunneling effect between quantum valley Hall edge states under an applied electric field in bilayer graphene containing gaps. A topological transistor based on this tunneling effect is proposed. In the on state of the transistor, the quantum valley Hall edge state along one bilayer-graphene zigzag edge can tunnel to the other edge under an electric field. In the off state without the electric field, the edge state cannot tunnel to the other edge and should be reflected by the top armchair edge and retrace the route along the same zigzag edge. The performance of the transistor is shown to be robust against long-range impurities. Compared with the previous transistor based on quantum spin Hall edge states [Xu et al. Phys. Rev. Lett. 123, 206801 (2019)], this transistor based on quantum valley Hall edge states has the advantages that it does not need a ferromagnetic gate to bridge the gap in the edge states and the conductance is robust against both nonmagnetic and magnetic impurities.