Half-Quantum Vortices in Thin Film of Superfluid $^3$He

TL;DR

This paper investigates the stability and formation conditions of half-quantum vortices in the A2 phase of superfluid helium-3 confined in thin films, using numerical solutions of the Ginzburg-Landau equations.

Contribution

It extends previous work by analyzing the stability of HQVs in the A2 phase within thin slab geometry and identifies conditions for their stable creation.

Findings

HQVs are stable near the A2-A1 phase boundary.

External magnetic fields of about 1 T are needed for stable HQV domains.

Temperature and magnetic field must be fixed before increasing angular velocity to form HQVs.

Abstract

Stability of a half-quantum vortex (HQV) in superfluid $^3$He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B {\bf 79}, 092506 (2009). We further extend this work here and consider the A$_2$ phase of superfluid $^3$He confined in thin slab geometry and analyze the HQV realized in this setting. Solutions of HQV and singly quantized singular vortex are evaluated numerically by solving the Ginzburg-Landau (GL) equation and respective first critical angular velocities are obtained by employing these solutions. We show that the HQV in the A$_2$ phase is stable near the boundary between the A$_2$ and A$_1$ phases. It is found that temperature and magnetic field must be fixed first in the stable region and subsequently the angular velocity of the system should be increased from zero to a sufficiently large value to create a HQV with sufficiently large probability. A HQV does not form if the system starts with a fixed angular velocity and subsequently the temperature is lowered down to the A$_2$ phase. It is estimated that the external magnetic field with strength on the order of 1 T is required to have a sufficiently large domain in the temperature-magnetic field phase diagram to have a stable HQV.