Half-quantum vortex pair in the polar-distorted B phase of superfluid He3 in aerogels

Abstract

Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connected by a Kibble-Lazarides-Shafi wall in superfluid $^{3}\mathrm{He}$ in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur in the polar-distorted $B$ (PdB) phase of superfluid $^{3}\mathrm{He}$. First, the ``impurity''-scattering model used in a previous study is extended to a form interpolating the weakly and strongly anisotropic cases, and it is found that, within the Ginzburg-Landau (GL) approach, Anderson's theorem is satisfied in the strongly anisotropic case. By taking account of the Fermi-liquid (FL) corrected gradient terms and solving numerically the resulting GL free energy, the anisotropy dependence of the vortex structure minimizing the free energy is examined within the weak-coupling approximation. 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 possible the emergence of a large HQV pair in the PdB phase, and that, nevertheless, such a large pair easily shrinks upon deeply entering 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.