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.}.
@article{arxiv.0905.2766,
title = {Gaps and tails in graphene and graphane},
author = {B. Dora and K. Ziegler},
journal= {arXiv preprint arXiv:0905.2766},
year = {2009}
}