Gaps and tails in graphene and graphane

TL;DR

This paper investigates how random symmetry-breaking potentials affect the density of states in graphene and graphane, revealing localized states that enable conduction despite the presence of gaps, aligning with recent experimental findings.

Contribution

It demonstrates that random potentials create tails in the density of states, which can close gaps and produce localized states, influencing conduction in graphene-based materials.

Findings

Random potentials induce tails in the density of states.

Localized states within the tails enable conduction at finite temperatures.

Results agree with recent experimental observations in graphane.

Abstract

We study the density of states in monolayer and bilayer graphene in the presence of a random potential that breaks sublattice symmetries. While a uniform symmetry-breaking potential opens a uniform gap, a random symmetry-breaking potential also creates tails in the density of states. The latter can close the gap again, preventing the system to become an insulator. However, for a sufficiently large gap the tails contain localized states with nonzero density of states. These localized states allow the system to conduct at nonzero temperature via variable-range hopping. This result is in agreement with recent experimental observations in graphane by Elias {\it et al.}.