Dislocation-induced superfluidity in a model supersolid

TL;DR

This paper investigates how edge dislocations in a Bose crystal can induce superfluidity, showing that superfluidity nucleates at dislocations before appearing in the bulk, and that dislocation networks significantly influence the supersolid transition temperature.

Contribution

It introduces a theoretical framework coupling dislocation strain fields to superfluidity, deriving a one-dimensional Landau equation, and models dislocation networks with an XY model, linking dislocation density to supersolid behavior.

Findings

Superfluidity nucleates at dislocations prior to bulk transition.

Dislocation density strongly affects the ordering temperature.

Theoretical results align with experimental observations of sample quality effects.

Abstract

Motivated by recent experiments on the supersolid behavior of $^4$He, we study the effect of an edge dislocation in promoting superfluidity in a Bose crystal. Using Landau theory, we couple the elastic strain field of the dislocation to the superfluid density, and use a linear analysis to show that superfluidity nucleates on the dislocation before occurring in the bulk of the solid. Moving beyond the linear analysis, we develop a systematic perturbation theory in the weakly nonlinear regime, and use this method to integrate out transverse degrees of freedom and derive a one-dimensional Landau equation for the superfluid order parameter. We then extend our analysis to a network of dislocation lines, and derive an XY model for the dislocation network by integrating over fluctuations in the order parameter. Our results show that the ordering temperature for the network has a sensitive dependence on the dislocation density, consistent with numerous experiments that find a clear connection between the sample quality and the supersolid response.