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 $G∕\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}=4n{e}^{2}∕h$, whereas for a zigzag edge the quantization changes to $G∕\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}=4(n+1∕2){e}^{2}∕h$, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}$ 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.