Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene

TL;DR

This paper investigates the effects of electromagnetic fields on massless Dirac fermions in 2D, revealing insights into topological phases, gauge invariance, and the minimal conductivity in graphene at finite temperature and density.

Contribution

It provides a detailed analysis of 1-loop quantum effects in planar QED, connecting Berry phases, gauge invariance, and conductivity in graphene.

Findings

Berry's phases depend on magnetic field invariance.

Effective Lagrangian is temperature and chemical potential independent under electric fields.

Predicted minimal conductivity matches experimental graphene values.

Abstract

We study 1-loop effects for massless Dirac fields in two spatial dimensions, coupled to homogeneous electromagnetic backgrounds, both at zero and at finite temperature and density. In the case of a purely magnetic field, we analyze the relationship between the invariance of the theory under large gauge transformations, the appearance of Chern-Simons terms and of different Berry's phases. In the case of a purely electric background field, we show that the effective Lagrangian is independent of the chemical potential and of the temperature. More interesting: we show that the minimal conductivity, as predicted by the quantum field theory, is the right multiple of the conductivity quantum and is, thus, consistent with the value measured for graphene, with no extra factor of pi in the denominator.