Eigenstate analysis of finite-frequency conductivity in graphene

• Published in: The European physical journal. B, Condensed matter physics Vol. 85; no. 10
• Main Author: Ray, R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.10.2012; EDP Sciences; Springer
• Subjects: Analysis; Complex Systems; Condensed Matter Physics; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electric properties; Electrical conductivity; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic transport in multilayers, nanoscale materials and structures; Exact sciences and technology; Fluid- and Aerodynamics; Graphene; Graphite; Localization effects (anderson or weak localization); Physics; Physics and Astronomy; Regular Article; Solid State Physics; Surface and interface electron states; Solid State and Materials; Eigenstates; Band structure; Kubo formula; Electrical conductivity; Fermi level; Graphene; Renormalization group method; Microscopic model; Square lattices; Carrier density; Disorder; Weak localisation
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2012-20885-8

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 l 2 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.