Double-Core Vortex Stabilized by Disorder in Superfluid $^3$He B Phase in Globally Isotropic Aerogel

In a p-wave Fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. Consequences of this divergent rigidity in the stable vortices in the B phase in globally isotropic aerogel are considered where the "impurity scattering" events are brought by the aerogel structure. For a moderately strong "impurity scatterings", the superfluid transition line T_c(P) has a quantum critical point at a low but finite pressure. We find that, with decreasing T_c via the lowering of the pressure, the distance between the half cores composing the core of the nonaxisymmetric double-core vortex which is stable at lower pressures grows as a result of the rigidity diverging at lowering temperature. The obtained result is compared with the elongation of the half core pair arising from the Fermi-liquid correction.