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

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.

5 pages, 5 figures