Absence of a metallic phase in charge-neutral graphene with a random gap

J. H. Bardarson, M. V. Medvedyeva, J. Tworzydlo, A. R. Akhmerov, C. W. J. Beenakker

Published 2010-02-03, updated 2010-02-04Version 2

It is known that fluctuations in the electrostatic potential allow for metallic conduction (nonzero conductivity in the limit of an infinite system) if the carriers form a single species of massless two-dimensional Dirac fermions. A nonzero uniform mass $\bar{M}$ opens up an excitation gap, localizing all states at the Dirac point of charge neutrality. Here we investigate numerically whether fluctuations $\delta M \gg \bar{M} \neq 0$ in the mass can have a similar effect as potential fluctuations, allowing for metallic conduction at the Dirac point. Our negative conclusion confirms earlier expectations, but does not support the recently predicted metallic phase in a random-gap model of graphene.