Random gap model for graphene and graphene bilayers

TL;DR

This paper investigates how random fluctuations in the energy gap affect the electronic properties of monolayer and bilayer graphene, revealing a transition to insulating behavior at a critical disorder level.

Contribution

It introduces a model for random gap fluctuations in graphene and bilayers, analyzing their impact on electronic states and transport properties using the self-consistent Born approximation.

Findings

Density of states vanishes at critical disorder level.

Transport properties weaken significantly in bilayer graphene.

Weak disorder effects in monolayer graphene.

Abstract

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 transport properties (diffusion coefficient and conductivity) are calculated at the neutrality point. All these quantities vanish at a critical value of the average staggered potential, signaling a continuous transition to an insulating behavior. The calculations are based on the self-consistent Born approximation for the one-particle scattering rate and a massless mode of the two-particle Green's function which is created by spontaneous symmetry breaking. Transport quantities are directly linked to the one-particle scattering rate. Moreover, the effect of disorder is very weak in the case of a monolayer but much stronger in bilayer graphene.