Superfluid $^3$He in globally isotropic random media

TL;DR

This paper investigates the A-like phase of superfluid $^3$He in globally isotropic aerogels, proposing a disordered ABM pairing state that maintains superfluidity despite lacking conventional long-range order.

Contribution

It introduces a theoretical model for superfluid $^3$He in isotropic aerogels, identifying a disordered ABM state as the ground state and analyzing vortex behavior using renormalization group methods.

Findings

Disordered ABM state is the most favorable pairing configuration.

Superfluidity persists despite absence of off-diagonal long-range order.

Coreless vortices are irrelevant to long-distance behavior.

Abstract

Recent theoretical and experimental studies of superfluid $^3$He in aerogels with a global anisotropy, e.g., due to an external stress, have definitely shown that the A-like phase with an equal spin pairing (ESP) in such aerogel samples is in the ABM (or, axial) pairing state. In this paper, the A-like phase of superfluid $^3$He in globally {\it isotropic} aerogel is studied in details by assuming a weakly disordered system in which singular topological defects are absent. Through calculation of the free energy, a disordered ABM state is found to be the best candidate of the pairing state of the globally isotropic A-like phase. Further, it is found through a one-loop renormalization group calculation that the coreless continuous vortices (or, vortex-skyrmions) are irrelevant to the long-distance behavior of the disorder-induced textures, and that the superfluidity is maintained in spite of lack of the conventional off-diagonal long range order. Therefore, the globally isotropic A-like phase at weak disorder is, like in the case with a global stretched anisotropy, a superfluid glass with the ABM pairing.