Exact eigenstate analysis of finite-frequency conductivity in graphene

TL;DR

This paper uses exact eigenstate methods to analyze finite-frequency conductivity in disordered graphene, revealing localization behavior, puddle formation, and agreement with experimental data at low disorder levels.

Contribution

It introduces an eigenstate basis formalism for graphene conductivity analysis, connecting with established theories and providing detailed insights into disorder effects.

Findings

States near the band center are more extended.

Conductivity at low disorder matches experimental observations.

Graphene localizes more easily than square lattices under disorder.

Abstract

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to the band centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away from the band centre. Further studies of current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. We calculate conductivity using Kubo Greenwood formula and show that, for low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparison with square lattice and find that graphene is more easily localized when subject to disorder.