Singular and Half-Quantum Vortices and Associated Majorana Particles in Superfluid 3He-A between Parallel Plates

TL;DR

This paper investigates the stability and properties of singular and half-quantum vortices in superfluid 3He-A confined between parallel plates, demonstrating conditions under which Majorana zero modes can exist in vortex cores, relevant to ongoing experiments.

Contribution

It establishes the phase diagram and stability conditions for vortices hosting Majorana modes in superfluid 3He-A using Ginzburg-Landau theory, including singular and half-quantum vortices.

Findings

Singular vortices with unit winding host Majorana modes.

Half-quantum vortices can also support Majorana zero modes.

Phase diagram maps vortex stability regions under rotation and system size.

Abstract

Motivated by a recent experiment on superfluid 3He-A confined in narrow parallel plates using a rotating cryostat, we explore possible vortices stable under magnetic field applied to arbitrary angle relative to the plates in order to seek vortices which can accommodate the Majorana zero mode in the core. After proving that the singular vortex with the unit winding number provides the Majorana mode in the spinful situation, we establish the phase diagram in the plane; the rotation frequency $\Omega$ vs system size R by finding possible order parameter textures within the Ginzburg-Landau framework. We also analyze the stability for a single and a pair of half-quantum vortices, which possesses the Majorana mode in its core. It is concluded from the above mention that the Majorana zero mode can be found in the present on-going experimental setting at ISSP, Univ. Tokyo.