Conductance quantization in mesoscopic graphene

Using a generalized Landauer approach we study the nonlinear transport in mesoscopic graphene with zigzag and armchair edges. We find that for clean systems, the low-bias low-temperature conductance, G, of an armchair edge system is quantized as G∕ ̃ \~t=4ne²∕h, whereas for a zigzag edge the quantization changes to G∕ ̃ \~t=4(n+1∕2)e²∕h, where ̃ \~t is the transmission probability and n is an integer. We also study the effects of a nonzero bias, temperature, and magnetic field on the conductance. The magnetic field dependence of the quantization plateaus in these systems is somewhat different from the one found in the two-dimensional electron gas due to a different Landau level quantization.