Dislocation-Mediated Melting in Superfluid Vortex Lattices

TL;DR

This paper models the thermal melting of vortex lattices in rotating superfluids using dislocation theory, deriving a melting temperature influenced by rotation and lattice properties, with implications for Bose-Einstein condensates.

Contribution

It generalizes the Halperin-Nelson theory to vortex lattices in superfluids, deriving a melting temperature dependent on shear modulus and rotation effects.

Findings

Melting temperature proportional to renormalized shear modulus.

Rotation attenuates lattice compression effects on dislocation energy.

Thermal melting occurs below Bose-Einstein transition temperature.

Abstract

We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -- rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.