Electronic structure of gated graphene and graphene ribbons

We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers n₂₃, the number of occupied subbands, and the density profiles as a function of the gate potential V₆. We discuss quantum corrections to the classical capacitance and we calculate the threshold V₆ above which semiconducting armchair ribbons conduct. We find that the ideal conductance of perfectly transmitting wide ribbons is proportional to the square root of the gate voltage.