Monte Carlo Study of the Semimetal-Insulator Phase Transition in Monolayer Graphene with a Realistic Interelectron Interaction Potential

We report on the results of the first-principles numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction, which takes into account the screening of Coulomb potential by electrons on $\sigma$ orbitals. In contrast to the results of previous numerical simulations with unscreened potential, we find that suspended graphene is in the conducting phase with unbroken chiral symmetry. This finding is in agreement with recent experimental results by the Manchester group [D. C. Elias et al., Nat. Phys. 7, 701 (2011); A. S. Mayorov et al., Nano Lett. 12, 4629 (2012)]. Further, by artificially increasing the interaction strength, we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.

Figure 1

A comparison of the partially screened Coulomb potential with the exact Coulomb potential and the potential obtained from noncompact gauge field on the hexagonal lattice [3].

Figure 2

The dependence of the chiral condensate (11) on $ϵ$ and on $m$ (in the inset) for the $18\times 18$ lattice with $N_t=20$ and $\delta =0.1{\mathrm{eV}}^{-1}$. For $ϵ=1.0$ we show the results obtained on the $24\times 24$ lattice with $N_t=40$, $\delta =0.05{\mathrm{eV}}^{-1}$.