Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

TL;DR

This paper calculates the a.c. conductivity of massless Dirac particles in graphene with Coulomb interactions in the collisionless regime, ensuring charge conservation and using dimensional regularization, resulting in a novel correction result.

Contribution

It provides a detailed, charge-conserving calculation of conductivity correction in graphene, differing from previous literature by employing a specific regularization method.

Findings

Derived a new correction for conductivity in graphene

Ensured Ward-Takahashi identities are satisfied

Used dimensional regularization with D=2-ε

Abstract

We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when \omega >> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by taking the spatial dimension D=2-\epsilon, for \epsilon > 0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.