Is graphene in vacuum an insulator?

TL;DR

This study uses lattice Monte Carlo simulations to investigate whether graphene in vacuum behaves as an insulator, finding evidence of a phase transition from semimetal to insulator at a specific Coulomb coupling strength.

Contribution

The paper provides the first lattice Monte Carlo evidence that vacuum graphene is likely an insulator, identifying the critical coupling and analyzing the phase transition nature.

Findings

Graphene in vacuum likely to be an insulator due to Coulomb interactions.

Identified critical Coulomb coupling for the semimetal-insulator transition as approximately 1.11.

Transition appears to be second-order, with a critical number of fermion flavors between 4 and 6.

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.