Chiral phases of superfluid 3He in an anisotropic medium

Recent advances in the fabrication and characterization of anisotropic silica aerogels with exceptional homogeneity provide new insight into the nature of unconventional pairing in disordered anisotropic media. 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 Anderson-Morel phase at T_c1 in which the chirality axis lî is aligned along the strain axis. This orbitally aligned state is protected from random fluctuations in the anisotropy direction, has a positive nuclear magnetic resonance (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_{c 1}. 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 one-dimensional "polar" order parameter to the two time-reversed two-dimensional axial Anderson-Brinkman-Morel 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 ξ_LIM 5μm at 18bar. I show that the random anisotropy results from mesoscopic structures in silica aerogels. This model for the random anisotropy field is coarse grained on the atomic scale, and is formulated in terms of local anisotropy in the scattering of quasiparticles in an aerogel with orientational correlations. Long-range order of locally anisotropic scattering centers is related to the splitting of the two ESP phases.