Coreless vortices in superfluidHe3-A: Topological structure, nucleation, and the screening effect

Abstract

Two simple relations connecting the superfluid circulation around any contour $C$ enclosing a simply connected surface $\Sigma$ and the texture in $\Sigma$ are established. They are applied to discuss the topological structures and the nucleation of coreless vortices in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$. It is shown that the latter is a very different phenomenon from the nucleation of singular vortices. A vortex ring of finite size, or a pair of antiparallel vortex lines separated by a finite distance, can be formed continuously out of a uniform order parameter. Their activation energy is connected intimately with the stability of superflow recently discussed. It vanishes near $T=0\mathrm{}$ but happens to be nonzero near $T_c$. It is also suggested that at any temperature $T<\mathrm{}{T}_c$ the absolute minimum of the free energy of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ in a container with a large surface circulation is given by a configuration with many coreless vortices confined in a tiny surface layer, so that in the bulk, the order parameter is a constant. This "screening effect," which affects strongly the amount of angular momentum carried by the fluid, is a special property of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$.