Competition between columnar pins and vortex screening: A doubly reentrant phase diagram

We study the phase diagram of flux lines in superconductors with columnar pins. Based on numerical exact diagonalization simulations on small clusters, we get two phases of vortices: A low-temperature pinned glass with diverging tilt modulus and a high-temperature delocalized entangled vortex liquid. For random potential disorder we find a new phase transition temperature T_BG from a pinned Bose glass to an entangled liquid that reduces with increasing vortex density. This occurs primarily because vortices screen the disorder potential and generate an effective weaker random potential with increasing vortex density. For a fixed fraction of randomly placed attractive columnar pins, we find a Mott-insulating phase when the vortex density exactly matches the density of pins at the matching field B=B_φ. We also find a transition from a strongly pinned Bose glass for B<B_φ to a weakly pinned Bose glass for B>B_φ as the vortex density is varied.