Coulomb interaction, ripples, and the minimal conductivity of graphene

TL;DR

This paper investigates how Coulomb interactions and ripples in graphene influence its minimal conductivity, revealing a universal logarithmic correction and a disorder-dependent finite contribution that aligns with experimental values.

Contribution

It demonstrates that unscreened Coulomb interactions cause a universal logarithmic correction to conductivity and shows how ripples and disorder affect the minimal conductivity in graphene.

Findings

Coulomb interactions provide a positive, universal, logarithmic correction to conductivity.

Disorder from ripples contributes a finite, non-universal increase to dc conductivity.

Theoretical minimal conductivity estimate aligns with experimental value near 4e^2/h.

Abstract

We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency. The combined effect of the disorder due to wrinkling of the graphene sheet and the long range electron-electron interactions is a finite positive contribution to the dc conductivity. This contribution is disorder strength dependent and thus non-universal. The low-energy behavior of such a system is governed by the line of fixed points at which both the interaction and disorder are finite, and the density of states is exactly linear. An estimate of the typical random vector potential representing ripples in graphene brings the theoretical value of the minimal conductivity into the vicinity of 4e^2/h.