Graphene's unique band structure has motivated much research toward a unified theory of graphene carrier transport. One of the outstanding mysteries, however, is graphene's residual conductivity. With a report by researchers at the University of Maryland, a fuller theoretical picture shows that the concentration of unavoidable impurities explains graphene's transport properties [Adam et al., Proc. Nat. Acad. Sci. USA (2007) 104, 18392].

Until now, the theory was that near the Dirac point (a singularity in the band structure where the density of states vanishes and carriers are massless Dirac fermions) graphene's charge carrier transport is ballistic and the conductivity minimum is a fixed quantity. But the new research shows unequivocally that the conductivity is a function of the concentration of impurities in the sample.

“Since we knew that the exfoliation technique used to obtain graphene involves extracting graphene onto a SiO₂ substrate and that the high density mobility is limited by dirt in the substrate and not in the graphene itself, we wanted to see if this would also explain the residual minimum conductivity,” says Shaffique Adam. “The basic idea is that the disorder induces carriers that in turn screen the impurities making them appear weaker.” Their theoretical framework to determine the residual density of carriers quantitatively solves the mystery of the residual conductivity.

A schematic of the model where charged impurities in the SiO₂ substrate give rise to puddles of electrons and holes whose carrier density needs to be calculated self-consistently. The researchers demonstrate that this residual density is responsible for the minimum conductivity. Also shown is a comparison between theory and experiment for a representative sample, where the only fitting parameter is the impurity concentration.

The work shows that the mobility below room temperature in current samples is set entirely by disorder in the substrate. Thus, changing the substrate or reducing impurities is the clear road to higher mobility – a promising idea for future graphene-based transistors. “By going to cleaner samples or suspended graphene,” says Adam, “we anticipate a whole host of new interesting physics that is the subject of our current research.”