Random-Gap Model for Graphene and Graphene Bilayers

The effect of a randomly fluctuating gap, created by a random staggered potential, is studied in a monolayer and a bilayer of graphene. The density of states, the one-particle scattering rate, and the transport properties (diffusion coefficient and conductivity) are calculated at the neutrality point. All of these quantities vanish at a critical value of the average staggered potential, signaling a continuous transition to an insulating behavior. Transport quantities are directly linked to the one-particle scattering rate. Although the behavior is qualitatively the same in mono- and bilayers, the effect of disorder is much stronger in the latter.