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

TL;DR

This study numerically investigates whether random mass fluctuations in charge-neutral graphene can induce metallic conduction, concluding that such fluctuations do not lead to a metallic phase, contrary to some recent predictions.

Contribution

The paper provides numerical evidence that random mass fluctuations do not produce a metallic phase in charge-neutral graphene, challenging recent theoretical predictions.

Findings

Random mass fluctuations do not induce metallic conduction.

A uniform mass opens an excitation gap and localizes states.

The results confirm the absence of a metallic phase in the random-gap model.

Abstract

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.