Diffusion and criticality in undoped graphene with resonant scatterers

TL;DR

This paper develops a comprehensive theory for charge transport in undoped graphene with various impurities, revealing how different impurity types affect conductivity and critical behavior.

Contribution

It introduces a general theoretical framework for analyzing impurity effects in graphene, enabling efficient numerical calculations of conductivity for different impurity classes.

Findings

Conductivity increases logarithmically with impurity concentration for smooth resonant impurities.

Conductivity saturates at a constant value for vacancies or strong on-site potential impurities.

The results align with renormalization group analysis for symmetry classes DIII and BDI.

Abstract

A general theory is developed to describe graphene with arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the minimal conductivity of graphene with resonant scatterers. In the case of smooth resonant impurities conductivity grows logarithmically with increasing impurity concentration, in agreement with renormalization group analysis for the symmetry class DIII. For vacancies (or strong on-site potential impurities) the conductivity saturates at a constant value that depends on the vacancy distribution among two sublattices as expected for the symmetry class BDI.