Electronic states, quantum hall effect and current profiles in graphene ribbons

We present a tight-binding continued-fraction description of the energy spectrum of zigzag and armchair graphene ribbons. The effect of a uniform magnetic field threading biased ribbons and the presence of top gates are also discussed. Stationary currents distribution is obtained by the nonequilibrium Keldysh-Green's function method. A pictorial description of conductive channels in the quantum Hall regime is provided. The analysis of the currents under applied gates shows that the Dirac-like nature of the states at the corners of the graphene Brillouin zone can be exploited to realize current manipulation.