Half-Quantum Vortex Pair in Polar-distorted B Phase of Superfluid 3He in Aerogels

TL;DR

This study investigates the intrinsic formation of large half-quantum vortex pairs in the polar-distorted B phase of superfluid 3He within aerogels, revealing the conditions under which they can occur without pinning effects.

Contribution

It provides a numerical analysis of vortex structures in superfluid 3He, highlighting the role of anisotropy and Fermi-liquid corrections in the emergence and stability of large HQV pairs.

Findings

Large HQV pairs can form near the polar-PdB phase transition due to anisotropy and Fermi-liquid effects.

Deep in the PdB phase, large HQV pairs tend to shrink without pinning effects.

The vortex structure is well described by the London limit, consistent with NMR measurements.

Abstract

Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connencted by a Kibble wall in superfluid 3He in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur with no pinning effect due to the aerogel structure in the polar-distorted B (PdB) phase of superfluid 3He. By fully examining the impurity-scattering induced pairing vertex, the emergence of Anderson's Theorem in the p-wave superfluid is verified in the two opposite limits, the isotropic and strongly anisotropic limits. Solving numerically the resulting Ginzburg-Landau (GL) free energy in the weak-coupling approximation and by taking account of the Fermi-liquid (FL) corrected gradient terms, the anisotropy dependence of the vortex structure minimizing the free energy is examined. It is found that, close to the transition between the polar and PdB phases, an interplay of the strong anisotropy and the FL correction makes emergence of a large HQV pair in the PdB phase possible, and that, nevertheless, such a large pair easily shrinks deep in the PdB phase, indicating that a pinning effect due to the aerogel structure is necessary in order to keep a large pair size there. The obtained result indicates the validity of the London limit for describing the vortex structure, and a consistency with the picture based on the NMR measurement is discussed.