Is graphene in vacuum an insulator?

Abstract

We present evidence, from Lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at $\alpha_g^\text{crit} = 1.11 \pm 0.06$, where $\alpha_g^{} \simeq 2.16$ in vacuum, and $\alpha_g^{} \simeq 0.79$ on a SiO$_2^{}$ substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors $4 < N_f^{\text{crit}} < 6$. Our data are consistent with a second-order transition.