Confinement of superfluid 3 He on length scales comparable to the radial size of the p-wave Cooper pairs can greatly alter the phase diagram by stabilizing broken symmetry phases not observed in bulk 3 He. We consider superfluid 3 He confined within long cylindrical channels of radius 100 nm, and report new theoretical predictions for the equilibrium superfluid phases under strong confinement. The results are based on the strong-coupling formulation of Ginzburg-Landau theory with precise numerical minimization of the free energy functional to identify the equilibrium phases and their regions of stability. We introduce an extension of the standard GL strong-coupling theory that accurately accounts for the phase diagram at high pressures, including the tri-crital point and TAB(p) line defining the region of stability for the bulk A-phase. We also introduce tuneable boundary conditions that allow us to explore boundary scattering ranging from maximal to minimal pairbreaking, and report results for the phase diagram as a function of pressure, temperature, and boundary conditions. Four stable phases are found: a polar phase stable in the vicinity of Tc, a strongly anisotropic, cylindrical analog of the bulk B phase stable at sufficiently low temperatures, and two chiral A-like phases with distinctly different orbital symmetry, one of which spontaneously breaks rotation symmetry about the axis of the cylindrical channel. The relative stability of these phases depends sensitively on pressure and the degree of pairbreaking by boundary scattering. The broken symmetries exhibited by these phases give rise to distinct signatures in transverse NMR resonance spectroscopy. We present theoretical results for the transverse NMR frequency shifts as functions of temperature, the rf pulse tipping angle and the static NMR field orientation.

Thin films of superfluid 3 He were predicted, based on weak-coupling BCS theory, to have a stable phase which spontaneously breaks translational symmetry in the plane of the film. This crystalline superfluid, or "stripe" phase, develops as a one dimensional periodic array of domain walls separating degenerate B phase domains. We report calculations of the phases and phase diagram for superfluid 3 He in thin films using a strong-coupling Ginzburg-Landau theory that accurately reproduces the bulk 3 He superfluid phase diagram. We find that the stability of the Stripe phase is diminished relative to the A phase, but the Stripe phase is stable in a large range of temperatures, pressures, confinement, and surface conditions.

Strong interactions that favor chiral p-wave pairing, combined with strong pair breaking by confining boundaries, are shown to lead to new equilibrium states with different broken symmetries. Based on a strong-coupling extension of the Ginzburg-Landau theory that accurately accounts for the thermodynamics and phase diagram of the bulk phases of superfluid ^{3}He, we predict new phases of superfluid ^{3}He for confined geometries that spontaneously break rotational and translational symmetry in combination with parity and time-reversal symmetry. One of the newly predicted phases exhibits a unique combination of chiral and helical order that is energetically stable in cylindrical channels of radius approaching the Cooper pair coherence length, e.g., R∼100  nm. Precise numerical minimization of the free energy yields a broad region of stability of the helical phase as a function of pressure and temperature, in addition to three translationally invariant phases with distinct broken spin and orbital rotation symmetries. The helical phase is stable at both high and low pressures and favored by boundaries with strong pair breaking. We present calculations of transverse NMR frequency shifts as functions of rf pulse tipping angle, magnetic field orientation, and temperature as signatures of these broken symmetry phases.

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid 3 He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of 3 He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid 3 He-B. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of H = 284 G parallel to the rotation axis, H Ω Ω Ω, are reported, as well as the supercooling transition line, T * V (p, H). In zero field the vortex phases of 3 He-B are separated by a first-order phase transition line T V (p) that terminates on the bulk critical line T c (p) at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly-quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and β phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, T * V (p, H), below which it is globally unstable to an array of D-core vortices. For H 60 G external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating 3 He-B, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating 3 He-B.

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