Model of Inhomogeneous Impurity Distribution in Fermi Superfluids

TL;DR

This paper introduces an inhomogeneous impurity scattering model for Fermi superfluids, specifically applied to superfluid 3He in aerogel, explaining experimental observations better than homogeneous models.

Contribution

The paper develops and applies an isotropic inhomogeneous scattering model to superfluid 3He, accounting for spatial impurity variations and improving agreement with experimental data.

Findings

Inhomogeneous model explains experimental data better than homogeneous theory.

Transition temperature and superfluid density are affected by impurity inhomogeneity.

Different temperature behaviors of the order parameter are identified.

Abstract

The standard treatment of impurities in metals assumes a homogeneous distribution of impurities. In this paper we study distributions that are inhomogeneous. We discuss in detail the "isotropic inhomogeneous scattering model" which takes into account the spatially varying scattering on the scale of the superfluid coherence length. On a large scale the model reduces to a homogeneous medium with renormalized parameter values. We apply the model to superfluid 3He, where porous aerogel acts as the impurity. We calculate the transition temperature Tc, the order parameter, and the superfluid density. Both A- and B-like phases are considered. Two different types of behavior are identified for the temperature dependence of the order parameter. We compare the calculations with experiments on 3He in aerogel. We find that most of the differences between experiments and the homogeneous theory can be explained by the inhomogeneous model. All our calculations are based on the quasiclassical theory of Fermi liquids. The parameters of this theory for superfluid 3He in aerogel are discussed.