Perturbative analysis of the conductivity in disordered monolayer and bilayer graphene

TL;DR

This paper provides a perturbative analysis of how different types of disorder affect the DC conductivity of monolayer and bilayer graphene, revealing cancellations and robustness in their conductive properties.

Contribution

It offers a detailed perturbative framework for understanding disorder effects on graphene's conductivity, including higher-order corrections and robustness in bilayer graphene.

Findings

Logarithmic divergences cancel in monolayer graphene for all disorder types.

Finite conductivity corrections occur for scalar potential and gap disorders in monolayer graphene.

Bilayer graphene's minimal conductivity remains unaffected by disorder due to complete cancellation.

Abstract

The DC conductivity of monolayer and bilayer graphene is studied perturbatively for different types of disorder. In the case of monolayer, an exact cancellation of logarithmic divergences occurs for all disorder types. The total conductivity correction for a random vector potential is zero, while for a random scalar potential and a random gap it acquires finite corrections. We identify the diagrams which are responsible for these corrections and extrapolate the finite contributions to higher orders which gives us general expressions for the conductivity of weakly disordered monolayer graphene. In the case of bilayer graphene, a cancellation of all contributions for all types of disorder takes place. Thus, the minimal conductivity of bilayer graphene turns out to be very robust against disorder.