The effect of disorder on the valley-dependent transport in zigzag graphene nanoribbons

We investigate the electron transport through a zigzag graphene nanoribbon with a staggered sublattice potential and a certain asymmetric boundary potential. By using the tight binding model to combine with the nonequilibrium Green’s function theory and the Landauer–Büttiker formalism, the energy band structure, conductance, and conductance fluctuation are calculated. We find that an energy gap opens up due to the inversion symmetry breaking by the staggered sublattice potential. By further tuning the boundary potential, the gapless valley-dependent edge states are achieved in which the carriers with the different valleys on a given boundary propagate in opposite directions. Furthermore, we study the effect of long range disorder on the transport properties of the valley-dependent edge states. The results show that the conductance plateau $4e2/h$ contributed by the edge states can be maintained well in a broad range of disorder strength for low-density disorder, indicating the robustness of the valley-dependent transport. In addition, the conductance fluctuation is also studied, and the fluctuation almost vanishes at weak disorder. On the other hand, at intermediate disorder strength with the system in the diffusive regime, the universal conductance fluctuation is exhibited. The conductance fluctuation is independent of various parameters, e.g., the ribbon width, the disorder range, and the disorder density.