Signatures of a gap in the conductivity of graphene

The electrical conductivity of suspended graphene has recently been measured for the first time, and found to behave as \sigma ~ \sqrt{|n|} as expected for Dirac quasiparticles at large carrier density. The charge inhomogeneity is strongly reduced in suspended samples, which revealed an unexpected insulating trend in \sigma(T). Above a transitional density n*, the temperature dependence was found to revert to metallic. We show that these features of the DC conductivity are consistent with a simple model of gapped Dirac quasiparticles, with specific signatures of a gap in the vicinity of the charge-neutrality point. Our findings are reminiscent of the conductivity profile in semiconducting materials, exhibiting a thermal activation for T \geq \tilde T and a weakly T-dependent background for T \leq \tilde T, where \tilde T is given by the saturation density \tilde n associated with the residual charge inhomogeneity. We discuss possible origins of a bandgap in graphene as well as alternative scenarios.