Chiral anomaly and strength of the electron-electron interaction in graphene

TL;DR

This paper demonstrates that electron-electron interactions in ideal graphene significantly enhance its electrical conductivity, with the effect linked to the chiral anomaly, providing clarity on a longstanding controversy.

Contribution

The study directly calculates the impact of electron-electron interactions on graphene's conductivity using a tight binding approach, clarifying the role of the chiral anomaly.

Findings

Conductivity is increased by a factor proportional to the interaction strength alpha.

The enhancement coefficient C is approximately 0.26.

The results resolve ambiguities related to the chiral anomaly in graphene.

Abstract

The long standing controversy concerning the effect of electron - electron interaction on the electrical conductivity of an ideal graphene sheet is settled. Performing the calculation directly in the tight binding approach without the usual prior reduction to the massless Dirac (Weyl) theory, it is found that, to leading order in the interaction strength alpha =e^2/(hbar*v0), the DC conductivity sigma/sigma0=1+C*alpha is significantly enhanced with respect to the independent-electrons result sigma0, i.e. with the value C = 0.26. The ambiguity characterizing the various existing approaches is nontrivial and related to the chiral anomaly in the system. In order to separate the energy scales in a model with massless fermions, contributions from regions of the Brillouin zone away from the Dirac points have to be accounted for. Experimental consequences of the relatively strong interaction effect are briefly discussed.