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.

Comments: 4 pages, 3 figures, published version