Numerical study of the conductivity of graphene monolayer within the effective field theory approach

TL;DR

This study uses numerical simulations within an effective field theory framework to measure graphene's conductivity, revealing a significant decrease in conductivity in the phase with broken sublattice symmetry.

Contribution

First direct numerical measurement of graphene's conductivity using lattice field theory and Maximum Entropy Method, highlighting phase-dependent conductivity behavior.

Findings

Conductivity drops rapidly in the broken symmetry phase.

At g=4.5, DC conductivity is at least 1000 times lower than in the weak-coupling phase.

Conductivity varies significantly with coupling strength.

Abstract

We report on the direct numerical measurements of the conductivity of graphene monolayer. Our numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1-dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. The conductivity is obtained from the Green-Kubo relations using the Maximum Entropy Method. We find that in a phase with spontaneously broken sublattice symmetry the conductivity rapidly decreases. For the largest value of the coupling constant used in our simulations g = 4.5, the DC conductivity is less than the DC conductivity in the weak-coupling phase (at g < 3.5) by at least three orders of magnitude.