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

TL;DR

This study uses Monte Carlo simulations within a tight-binding model to analyze how Coulomb interactions affect the electronic transport in monolayer graphene, revealing a phase transition at strong coupling.

Contribution

It introduces a lattice gauge theory approach with Hybrid Monte Carlo to investigate Coulomb effects on graphene's conductivity, highlighting a spontaneous symmetry breaking at strong coupling.

Findings

At strong coupling (e<4), symmetry breaks and conductivity drops to 20-30% of the weak-coupling value.

In weak coupling (e>4), conductivity remains nearly constant and close to the universal value 1/4.

The phase transition occurs at a critical dielectric permittivity around e≈4.

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 non-compact 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 e<4, and at sufficiently small temperatures T<10^4 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 e>4) the conductivity practically does not depend on e and is close to the universal value s=1/4.