Half-Quantum Vortices in Thin Film of Superfluid 3He
Abstract
Stability of a half-quantum vortex (HQV) in superfluid 3He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B 79, 092506 (2009). We further extend this work here and consider the A2 phase of superfluid 3He 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 A2 phase is stable near the boundary between the A2 and A1 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 A2 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.
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