Localization and Kosterlitz-Thouless Transition in Disordered Graphene

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.