Delocalization in two dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate the existence of the intermediate superfluid state where the condensate and localized bosons present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto the three dimensional system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning transition within the vortex liquid and depinning induced vortex lattice/Bose glass melting.