  Using a generalized Landauer approach we study the non-linear transport in
mesoscopic graphene with zig-zag and armchair edges. We find that for clean
systems, the low-bias low-temperature conductance, G, of an armchair edge
system in quantized as G/t=4 n e^2/h, whereas for a zig-zag edge the
quantization changes to G/t t=4(n+1/2)e^2/h, where t is the transmission
probability and n is an integer. We also study the effects of a non-zero 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.
