Localization and Kosterlitz-Thouless Transition in Disordered Graphene

TL;DR

This paper studies how strong long-range disorder causes localization in graphene near the Dirac points, revealing a Kosterlitz-Thouless transition driven by vortex dynamics, challenging previous beliefs about delocalization in such systems.

Contribution

It demonstrates the occurrence of a Kosterlitz-Thouless transition in disordered graphene, highlighting the role of vortex binding in localization phenomena.

Findings

States near Dirac points become localized with strong disorder

The transition is of Kosterlitz-Thouless type involving vortex unbinding

Localization occurs despite expectations of delocalization in 2D Dirac systems

Abstract

We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is ex-pected to be equivalent to a disordered two-dimensional Dirac Fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.