The bond charge current in the monolayer graphene superlattice with hopping beyond nearest neighbor

In this paper, we systematically investigate the transportation properties of the zigzag nano-ribbon graphene in a local potential barrier/well with electrons hopping between and beyond nearest neighbor. When the local potential is present, the conductance exhibits novel periodic oscillation plateaus around increasing quantized conductance. The oscillation plateau hops down with the quantized conductance until vanishes with increasing local potential barrier. Furthermore, when a small voltage is applied between the two terminals of the conductor, the local current presents periodic oscillation in the barrier region. In contrast, when a local potential well is applied, the conductance shows irregular oscillation, exhibiting incommensurate oscillations of local current inside and outside the well. Finally, similar phenomena persists when more local potentials are applied to the system. We expect our studies can facilitate the design of relevant electronic devices.