Interaction corrections to the minimal conductivity of graphene via dimensional regularization

TL;DR

This paper calculates the two-loop interaction correction to the minimal conductivity of pristine graphene using dimensional regularization, providing results consistent with experiments and resolving previous theoretical disagreements.

Contribution

It presents a novel two-loop calculation of graphene's minimal conductivity correction using dimensional regularization, clarifying previous theoretical disputes.

Findings

Interaction correction is approximately 1% of the minimal conductivity.

Results are consistent with experimental uncertainties.

The calculation resolves a prior theoretical dispute.

Abstract

We compute the two-loop interaction correction to the minimal conductivity of disorder-free intrinsic graphene with the help of dimensional regularization. The calculation is done in two different ways: via density-density and via current-current correlation functions. Upon properly renormalizing the perturbation theory, in both cases, we find that: $\sigma = \sigma_0\,( 1 + \al\,(19-6\pi)/12) \approx \sigma_0 \,(1 + 0.01\, \al)$, where $\al = e^2 / (4 \pi \hbar v)$ is the renormalized fine structure constant and $\sigma_0 = e^2 / (4 \hbar)$. Our results are consistent with experimental uncertainties and resolve a theoretical dispute.