Spontaneous helical order of a chiral p-wave superfluid confined in nano-scale channels

TL;DR

This paper predicts new equilibrium phases of superfluid $^3$He confined in nano-scale channels, including a stable helical phase with unique symmetry-breaking properties, using a strong-coupling Ginzburg-Landau theory.

Contribution

It introduces a theoretical prediction of a spontaneously formed helical phase of superfluid $^3$He in confined geometries, expanding understanding of symmetry-breaking in quantum fluids.

Findings

Identification of a stable helical phase in cylindrical channels of ~100 nm radius.

Prediction of multiple broken symmetry phases with distinct spin and orbital properties.

Calculation of NMR signatures as experimental indicators of these phases.

Abstract

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 Ginzburg-Landau (GL) 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. $R\sim 100\,\mbox{nm}$. Precise numerical mimimization of the GL 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.