Dislocation-induced superfluidity in a model supersolid

The effect of an edge dislocation in inducing superfluidity is explored by coupling the elastic strain field of the dislocation to the superfluid density, and solving the corresponding Ginzburg-Landau theory. It is shown that superfluid density is induced along a single dislocation below a critical temperature determined by the ground state solution of a 2D Schr\"odinger equation with a dipolar potential. This superfluid behavior can be described by a 1D Ginzburg-Landau equation obtained through a weakly nonlinear analysis. We then extend our analysis to a network of dislocation lines considered before by Shevchenko and Toner, which could serve as a model for superflow through solid $^4$He. The effect of fluctuations and dynamics are included through a full time dependent Ginzburg-Landau theory.