Monte Carlo study of the electron transport properties of monolayer graphene within the tight-binding model

Abstract

We study the effect of Coulomb interaction between charge carriers on the properties of graphene monolayer, assuming that the strength of the interaction is controlled by the dielectric permittivity of the substrate on which the graphene layer is placed. To this end, we consider the tight-binding model on the hexagonal lattice coupled to the noncompact gauge field. The action of the latter is also discretized on the hexagonal lattice. Equilibrium ensembles of gauge field configurations are obtained using the hybrid Monte Carlo algorithm. Our numerical results indicate that at sufficiently strong coupling, that is, at sufficiently small substrate dielectric permittivities $\ensuremath{\epsilon}\ensuremath{\lesssim}4$ and at sufficiently small temperatures $T\ensuremath{\lesssim}1\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the symmetry between simple sublattices of hexagonal lattice breaks down spontaneously and the low-frequency conductivity gradually decreases down to $20--30%$ of its weak-coupling value. On the other hand, in the weak-coupling regime (with $\ensuremath{\epsilon}\ensuremath{\gtrsim}4$), the conductivity practically does not depend on $\ensuremath{\epsilon}$ and is close to the universal value ${\ensuremath{\sigma}}_{0}=1/4$.