Field-Induced Kosterlitz-Thouless Transition in the N=0 Landau Level of Graphene

At the charge neutral point, graphene exhibits a very unusual high-resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the XY valley-pseudospin order parameter, a situation which is dual to a conventional thin superconducting film. We study energetics and the stability of this phase in the presence of disorder.