Interstitials, vacancies, and dislocations in flux-line lattices: a theory of vortex crystals, supersolids, and liquids

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.