Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons

We employ the formalism of bond currents, expressed in terms of the nonequilibrium Green functions, to image the charge flow between two sites of the honeycomb lattice of graphene ribbons of few nanometers width. In sharp contrast to nonrelativistic electrons, current density profiles of quantum transport at energies close to the Dirac point in clean zigzag graphene nanoribbons (ZGNR) differs markedly from the profiles of charge density peaked at the edges due to zero-energy localized edge states. For transport through the lowest propagating mode induced by these edge states, edge vacancies do not affect current density peaked in the center of ZGNR. Furthermore, the long-range potential of a single impurity placed in the center of ZGNR acts to reduce local current around it while concurrently increasing the current density along the zigzag edge, so that ZGNR conductance remains perfect $G = 2e^{2}/h$