Half quantum vortex in superfluid $^3$He-A phase in parallel plate geometry

TL;DR

This paper investigates the stability and experimental signatures of half quantum vortices in superfluid helium-3 A phase confined between parallel plates, providing theoretical support for recent experimental observations.

Contribution

It offers a theoretical analysis demonstrating the stability of bound HQVs in a specific geometry and explains NMR signals as evidence of their existence.

Findings

Bound HQVs are more stable than singular vortices below a critical rotation speed.

Tilted ${ m f d}$-vector causes additional NMR absorption.

Results support the experimental detection of HQVs in superfluid $^3$He.

Abstract

The half quantum vortex(HQV) in condensate has been studied, since it was predicted by Salomaa and Volovik in superfluid $^3$He-A phase. However, an experimental evidence for its existence has not been reported so far. Motivated by a recent experimental report by Yamashita et al\cite{yamashita}, we study the HQVs in superfluid $^3$He confined between two parallel plates with a gap D $\sim$ 10 $\mu$m in the presence of a magnetic field H $\sim$ 26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, $\Omega_c \sim$ 2 rad/s. The bound pair of HQVs accompanies the tilting of ${\hat d}$-vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in $^3$He.