Zero Energy Modes and Statistics of Vortices in Spinful Chiral p-Wave Superfluids

TL;DR

This paper investigates the stability and statistics of vortices in spinful chiral p-wave superfluids, focusing on Majorana zero modes and their non-Abelian braiding properties, using theoretical models and calculations.

Contribution

It provides a detailed analysis of vortex stability regions and conditions for realizing non-Abelian Majorana modes in superfluid $^3$He-A.

Findings

Existence of Majorana zero modes in certain vortex configurations.

Conditions for non-Abelian statistics depend on external parameters.

Stability regions mapped in pressure, temperature, and field space.

Abstract

The possible stable singular vortex (SV) and half-quantum vortex (HQV) of the superfluid $^3$He-A phase confined in restricted geometries are investigated. The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics. The energetics between those vortices is carefully examined using the standard Ginzburg-Landau (GL) functional with a strong-coupling correction. The Fermi liquid effect, which is not included in the GL functional, is considered approximately within the London approach. This allows us to determine the stability regions in pressure, temperature, and applied field for SV and HQV. The existence of the Majorana zero mode and its statistics, either Abelian or non-Abelian under braiding of SVs, is studied by solving the Bogoliubov-de Gennes equation for spinful chiral p-wave superfluids at sufficiently low temperatures. We determined several conditions controllable external parameters for realizing the non-Abelian statistics of Majorana zero modes e.g., pressure, field direction, and strength.