Dislocations and the critical endpoint of the melting line of vortex line lattices

We develop a theory for dislocation-mediated structural transitions in the vortex lattice which allows for a unified description of phase transitions between the three phases, the elastic vortex glass, the amorphous vortex glass, and the vortex liquid, in terms of a free-energy functional for the dislocation density. In the presence of point defects, the existence of a critical endpoint of the first-order melting line at high magnetic fields, which has been recently observed experimentally, is explained.