Macroscopic Phase Coherence of Defective Vortex Lattices in Two Dimensions

Abstract

The superfluid density is calculated theoretically for incompressible vortex lattices in two dimensions that have isolated dislocations quenched in by a random arrangement of pinned vortices. The latter are assumed to be sparse and to be fixed to material defects. It is shown that the pinned vortices act to confine a single dislocation of the vortex lattice along its glide plane. Plastic creep of the two-dimensional vortex lattice is thereby impeded, and macroscopic phase coherence results at low temperature in the limit of a dilute concentration of quenched-in dislocations.