Disorder and interaction effects in two dimensional graphene sheets

TL;DR

This paper investigates how disorder and electron-electron interactions influence the low-temperature properties of two-dimensional graphene sheets using Renormalization Group methods, revealing stable and unstable fixed points related to different disorder types.

Contribution

It provides a detailed RG analysis of disorder and interaction effects in graphene, identifying conditions for stable and unstable fixed points and analyzing mid-gap states near interfaces.

Findings

Stable fixed points occur with topological disorder or random mass.

Unstable fixed points are associated with impurity-induced disorder.

Mid-gap states can form near interfaces or vacancies.

Abstract

The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points where the strength of the interactions remains finite, as in one dimensional Luttinger liquids. These fixed points can be either stable (attractive), when the disorder is associated to topological defects in the lattice or to a random mass term, or unstable (repulsive) when the disorder is induced by impurities outside the graphene planes. In addition, we analyze mid-gap states which can arise near interfaces or vacancies.