A–B transition of superfluid ${}^3\text{He}$ in aerogel under magnetic field

Abstract

A–B phase transition of superfluid ${}^3\text{He}$ in aerogel under magnetic field is discussed using the homogeneous impurity model. The second-order A–B transition temperature T_AB is calculated in the whole temperature range as a function of the magnetic field. It is shown that the GL result is correct only in the vicinity of the transition temperature T_ca of the liquid ${}^3\text{He}$ in aerogel.

Introduction

Since the discovery of the superfluidity of liquid ${}^3\text{He}$ in aerogel, there has been considerable interest in impurity scattering effects on p-wave superfluid. Clear evidence of the impurity scattering effect has been observed as the reduction of the superfluid transition temperature and the superfluid density. However, the identification of the order parameter structure and the modification of the phase diagram have not yet been established. In the p-wave spin-triplet pairing systems under magnetic field, A-phase with equal-spin pairs is more favorable than the B-phase that has ↑↓+↓↑ pairs as well. Such an A–B transition under magnetic field has been observed in the superfluid phase of ${}^3\text{He}$ in aerogel [1], [2]. Brussaard et al. measured the superfluid density ρ_s in aerogel under magnetic fields using a vibrating wire technique and found a clear signature of A–B transition as an abrupt change in ρ_s. Gervais et al. succeeded in detecting multiple phase transitions of the ${}^3\text{He}$-aerogel system in magnetic fields using high-frequency sound.

In this paper we present a theoretical study of impurity scattering effect on the phase diagram under magnetic field on the basis of the homogeneous impurity model [3]. We calculate the A–B transition line over the whole temperature range using the self-consistent order parameter within the weak coupling theory.