Universal conductivity of graphene in the ultra-relativistic regime

TL;DR

This paper calculates the universal optical conductivity of clean graphene in the ultra-relativistic regime where electromagnetic retardation effects are significant, revealing corrections to the non-interacting value and providing detailed theoretical results.

Contribution

It introduces a comprehensive calculation of graphene's optical conductivity considering electromagnetic retardation effects and Lorentz symmetry, extending beyond previous Coulomb interaction models.

Findings

Universal correction to conductivity proportional to fine structure constant

First order correction coefficient of order one

Conductivity results in the large-N limit up to order 1/N^2

Abstract

We calculate the optical (cutoff >> frequency >> temperature) conductivity in clean graphene in the ultimate low-energy regime, when retardation effects of the electromagnetic interaction become important and when the full Lorentz symmetry emerges. In contrast to what happens with the short range or with the Coulomb long-range instantaneous interactions, the optical conductivity is now no longer equal to its non interacting value, but acquires universal corrections in powers of the fine structure constant. The coefficient of the first order correction is computed, and found to be of order one. We also present the result for the conductivity in the large-N limit, with $N$ as the number of Dirac fermions species, to the order $1/N^2$.