Thermal phase transition in two-dimensional disordered superconductors

Weakly disordered two-dimensional superconductors undergo a Kosterlitz-Thouless (KT) transition, where at a critical temperature vortices proliferate through the system and destroy the superconducting (SC) order. On the other hand, it was suggested that for large disorder the system separates into regions of high SC order, and it is the percolation of coherence between these regions that is lost at the critical temperature. Here we demonstrate that both these descriptions can be applied, suggesting that they are the dual of each other. A vortex causes loss of local correlations, and thus the loss of percolation of correlations is concomitant with percolation of vortices on the dual lattice, in the perpendicular direction, i.e. the KT transition.