Strong Coupling Correction in Superfluid $^3$He in Aerogel

TL;DR

This paper investigates how impurity scattering affects the strong coupling contributions to superfluid $^3$He in aerogels, revealing impurity scattering favors the Balian-Werthamer (BW) state and reduces the ABM phase region, aligning with experimental phase diagrams.

Contribution

It provides a theoretical analysis of impurity effects on strong coupling corrections in superfluid $^3$He, using two approaches to explain experimental observations.

Findings

Impurity scattering favors the BW pairing state.

The ABM phase region shrinks due to impurity effects.

The results justify experimentally observed phase diagrams.

Abstract

Effects of impurity scatterings on the strong coupling (SC) contribution, stabilizing the ABM (axial) pairing state, to the quartic term of the Ginzburg-Landau (GL) free energy of superfluid $^3$He are theoretically studied to examine recent observations suggestive of an anomalously small SC effect in superfluid $^3$He in aerogels. To study the SC corrections, two approaches are used. One is based on a perturbation in the short-range repulsive interaction, and the other is a phenomenological approach used previously for the bulk liquid by Sauls and Serene [Phys.Rev.B 24, 183 (1981)]. It is found that the impurity scattering favors the BW pairing state and shrinks the region of the ABM pairing state in the T-P phase diagram. In the phenomenological approach, the resulting shrinkage of the ABM region is especially substantial and, if assuming an anisotropy over a large scale in aerogel, leads to justifying the phase diagrams determined experimentally.