Gate-tunable localization and delocalization of perfect valley-related topological edge states in zigzag graphene nanoribbons

Abstract

We investigated the properties of the energy band and edge states of zigzag graphene nanoribbons with side gates and staggered sublattice potential. The staggered sublattice potential can introduce a bulk band gap, and there are flat bands directly connecting two Dirac points at the edge of the band gap. The addition of the side gate can make the flat band as a whole enter the bulk band gap, forming a transportable edge state, and because of the existence of the flat band, these transportable edge states are all localized near the two Dirac points, a helical edge state structure related to the valley is formed. Through the analysis of non-equilibrium Green’s function, it is found that these valley-related edge states can lead to quantized Hall conductance. However, it should be emphasized that the edge states related to the valley Hall effect are not sensitively dependent on the depth of the flat band in the bulk band gap. Further by analyzing the relationship between the current of the system and the side gate, we found that the system has a very good topological edge state switching effect.