Gaps and tails in graphene and graphane

We study the density of states (DOS) in monolayer and bilayer graphene in the presence of a random potential that breaks sublattice symmetries. While a uniform symmetry-breaking potential (SBP) opens a uniform gap, a random SBP also creates tails in the DOS. The latter can close the gap again, preventing the system from becoming an insulator. However, for a sufficiently large gap the tails contain localized states with nonzero DOS. 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 et al (2009 Science 323 610).