Superfluid transition in a correlated defect network

TL;DR

This paper models superfluidity in a defected solid with correlated dislocations, revealing a new universality class with a less singular transition, relevant to supersolid behavior in helium-4.

Contribution

It introduces a novel theoretical framework for superfluid transition in defect networks, incorporating correlated disorder effects and numerical validation.

Findings

Disorder shifts the superfluid transition to a new universality class.

Correlation length exponent $ u \,\geq 1$ indicates altered critical behavior.

Transition exhibits finite derivatives of superfluid density and heat capacity at $T_c$.

Abstract

Motivated by recent experiments on possible supersolid behavior of $^4$He solids at low temperature, we consider a model of superfluidity in a defected solid containing a system spaning network of correlated linear dislocations, or planar grain boundaries. Using arguments based on the Harris criterion, as well as numerical simulations, we find that such correlated quenched disorder shifts the familiar superfluid lambda transition to a new disordered universality class in which the correlation length exponent $\nu\ge 1$. This results in the temperature-derivates for the superfluid density, $d\rho_{\rm s}/dT$, and for the heat capacity, $dc/dT$, remaining finite at the transition $T_{\rm c}$, and thus a less singular transition, profoundly different from the usual lambda transition.