Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids

TL;DR

This paper develops a theoretical framework for vortex matter in type-II superconductors, analyzing how vacancies, interstitials, and dislocations affect the elastic properties and phase behavior of flux-line lattices, including transitions to liquid and hexatic states.

Contribution

It introduces a comprehensive theory describing the impact of defects on vortex lattice elasticity and phase transitions, linking dislocation dynamics to vortex liquid and hexatic phases.

Findings

Vacancies and interstitials modify elastic moduli of vortex lattices.

Dislocation loops cause the shear modulus to vanish.

The long-wavelength properties resemble a flux-line hexatic phase.

Abstract

We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally identical to that of the ``flux-line hexatic'' that is a candidate ``normal'' hexatically ordered vortex liquid state.