Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints

TL;DR

This paper calculates the Coulomb correction to the ac conductivity of massless Dirac particles in graphene, resolving regularization ambiguities through symmetry constraints, and provides an exact value within the effective model.

Contribution

It introduces a regularization-independent method to determine the Coulomb correction in graphene's conductivity using symmetry constraints, clarifying previous discrepancies.

Findings

Coulomb correction $ ext{C} = (19 - 6 ext{pi})/12$ is precisely determined.

Symmetry constraints fix regularization-dependent parameters.

Comparison with other regularizations explains differences in literature results.

Abstract

We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6\pi)/12$ within this effective model. We compare our result with explicit regularizations and discuss the origin of others results for $\mathcal{C}$ found in the literature.