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

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 $\overline{M}$ opens up an excitation gap, localizing all states at the Dirac point of charge neutrality. Here we investigate numerically whether fluctuations $\ensuremath{\delta}M⪢\overline{M}\ensuremath{\ne}0$ 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.