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

line merge. 14 In this paper we present an explanation for the existence of a critical endpoint of the first-order melting line in the presence of point disorder. Our argumentation is based on a unified description of the vortex lattice phases. We demonstrate that all phase transitions between vortex lattice phases can be described as dislocation mediatedby deriving the free energy for an ensemble of directed dislocations as a function of the dislocation density in the presence of thermal and disorder. Each of the experimentally observed phases is characterized by its inherent dislocation density or, equivalently, by the characteristic dislocation spacing RD . The elastic VG is dislocation-free and has RD5‘. The VL can be viewed as a vortex array saturated with dislocations such that RD;a, and in the amorphous VG, R D ;R a , where R a is the socalled positional correlation length on which typical vortex displacements are of the order of the lattice spacing a. 2 Within our approach each phase corresponds to one of the local minima in the dislocation ensemble free energy, and dislocation densities in these minima represent the equilibrium dislocation densities in the corresponding phases. The global minimum corresponds to the thermodynamically stable phase under the given conditions, phase transitions occur when two local minima exchange their role as global minimum. This mechanism for the transitions enables us to derive Lindemann-criteria both for the locations of the thermal melting line and for the disorder-induced instability line of the BrG. Furthermore, the characteristic scale set by the mean distance between free dislocations offers a natural explanation of the critical endpoint of the first-order melting line: While at low magnetic fieldsRa@a and the amorphous VG appears to contain significantly less dislocations than the VL, at higher field where R a 5a the two phases become thermodynamically equivalent and the first-order melting line has to terminate.