We study the local structure of an Abrikosov vortex centered in a mesoscopic diffusive superconducting granule within the Usadel framework. We show that the spatial dependence of the pair potential, supercurrent, and local density of states near the vortex center is governed by a single parameter, leading to universal behavior in the core region. This parameter also controls discontinuities in these quantities at the interface between the grain and the surrounding superconductor. We further derive an explicit criterion for vortex existence in an isolated grain, yielding a critical radius R c ≈ 3.47ξ s at T → 0 and R c ≈ 1.84ξ( T ) in the Ginzburg–Landau limit. The obtained results enable the extraction of interface parameters from spectroscopic data.
Golubov et al. (Sun,) studied this question.