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

Abstract

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 σ 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.

Chirald-wave superconductivity in doped graphene

“…Another variant of RG flows are temperature flows, where by a rescaling of the terms in the action, the RG describes the evolution of the interactions when the temperature is lowered. Then, the right hand side of the flow equation (16) instead has temperature-derivatives of the one-loop diagrams.…”

“…The effective fine structure constant then becomes α = e 2 v F ≈ 0.9. This is, according to hybrid Monte Carlo simulations, in close proximity to the α needed for an insulating transition in graphene due to the long-range Coulomb interaction [66,12,16]. Taken together, these results show that both the short-range and longrange Coulomb interactions in graphene are likely sufficiently strong to, at the very least, put pristine graphene relatively close to a transition to an ordered ground state, which, somewhat depending on the exact nature of the short-range interaction, will have an antiferromagnetic spin ordering.…”

“…[4,5,6,7,8,9,10,11,12,13,14,15,17,16]). There, the predominant ordering tendencies are in the particle-hole channel, and usually superconductivity is not among the leading candidates.…”

“…A large number of exotic states of matter has been proposed theoretically, see e.g. [4,5,6,7,8,9,10,11,12,13,14,15,16,17], but most have not been experimentally observed as of yet. One exception is multi-layer graphene systems where there are now experimental reports of an energy gap opening at low temperatures, which has been ascribed to interactions effects [18,19,20,21,22,23,24,25].…”

In memory of Mikhail Igorevich Polikarpov

“…In [19] a first-principle numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction was performed. For the first time the screening of Coulomb potential by electrons on σ -orbitals was taken into account.…”