Spontaneous Helical Order of a Chiral p-Wave Superfluid Confined in Nanoscale Channels

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.