Chiral Phases of Superfluid 3He in an Anisotropic Medium

TL;DR

This paper develops a Ginzburg-Landau theoretical framework to predict and analyze the equilibrium chiral phases of superfluid 3He in uniaxial aerogel, identifying distinct phases and their experimental signatures.

Contribution

It introduces a novel GL theory for superfluid 3He in anisotropic media, predicting a sequence of phase transitions and specific NMR signatures for each phase.

Findings

Prediction of a chiral ABM phase with positive NMR shift in stretched aerogel.

Identification of a biaxial phase breaking axial symmetry at lower temperature.

Estimation of orbital domain size (~5 μm) from NMR frequency shift data.

Abstract

I report theoretical analysis and predictions for the equilibrium phases of superfluid 3He infused into a low-density, homogeneous uniaxial aerogel. Ginzburg-Landau (GL) theory for a class of equal-spin-pairing (ESP) states in a medium with uniaxial anisotropy is developed and used to analyze recent experiments on uniaxially strained aerogels. For 3He in an axially "stretched" aerogel GL theory predicts a transition from normal liquid into a chiral ABM phase at T_c1 in which the chirality axis, l, is aligned along the strain axis. This orbitally aligned state, is protected from random fluctuations in the anisotropy direction, has a positive NMR frequency shift, a sharp NMR resonance line and is identified with the high-temperature ESP-1 phase of superfluid 3He in axially stretched aerogel. A second transition into a biaxial phase is predicted to onset at a slightly lower temperature, T_c2 < T_c1. This phase is an ESP state, breaks time-reversal symmetry, and is defined by an orbital order parameter that spontaneously breaks axial rotation symmetry. This transition is driven by the coupling of an axially aligned 1D "polar" order parameter to the two time-reversed 2D axial ABM states. The biaxial phase has a continuous degeneracy associated with the projection of its chiral axis in the plane normal to the anisotropy axis. Theoretical predictions for the NMR frequency shifts of the biaxial phase provide an identification of the ESP-2 as the biaxial state, partially disordered by random anisotropy (Larkin-Imry-Ma effect). The "width" of the jump in the NMR frequency shift at T_c2 provides an estimate of the orbital domain size, xi_LIM ~ 5 mu-m at 18 bar.