Eur. Phys. J. B (2012) 85: 334
https://doi.org/10.1140/epjb/e2012-20885-8

Regular Article

Eigenstate analysis of finite-frequency conductivity in graphene

Department of Physics, Indian Institute of Technology Kanpur, 208016 Kanpur, India

^a e-mail: rray@iitk.ac.in

Received: 31 October 2011
Received in final form: 14 March 2012
Published online: 1 October 2012

Abstract

Eigenstate bases are used to study electrical conductivity in graphene in the presence of short-range diagonal disorder and inter-valley scattering. For the first time, the behavior of graphene in a moderate and weak disorderd regime is presented. For disorder strength, W / t ≥  5, the density of states is flat. A connection is then established with the work of Abrahams et al. using Microscopic Renormalization Group (MRG) approach. For disorder strength, W / t = 5, results are in good agreement. For low disorder strength, W / t = 2, energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre is studied. Explicit dependence of the current matrix elements on Fermi energy is shown. It is found that states close to the band centre are more extended and fall off nearly as 1/E_l² as one moves away from the band centre. Further studies on current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. Using the Kubo-Greenwood formula, conductivity and mobility is calculated. 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 comparision with square lattice and find that graphene is more easily localized when subject to disorder.