Abrikosov vortices are among the most fundamental manifestations of superconductivity. Their internal structure contains valuable information about the microscopic properties of the superconducting state and can now be directly visualized by scanning tunneling microscopy (STM) with atomic-scale resolution.

In this work, we investigate how the structure of a vortex is modified when it is trapped inside a mesoscopic superconducting grain connected to its surroundings through a finite-transparency interface. Using the quasiclassical Usadel theory, we show that the pair potential, supercurrent density, and local density of states exhibit abrupt changes at the grain boundary. Remarkably, in the experimentally relevant limit of small grains, these interface effects are governed by a single dimensionless parameter that combines the grain size and interface transparency.

Our theory predicts a characteristic jump in the local density of states at the grain boundary, which can be directly measured by STM. This provides a practical route for extracting the intergranular boundary resistance from spectroscopic data. We also derive an analytical criterion determining the minimum grain size required to support a vortex state.

The results establish a simple framework for interpreting vortex-core spectroscopy in granular superconductors and reveal how local superconducting properties can be inferred from the electronic structure of individual vortices.

A.A.Golubov, M.M.Khapaev, V. S. Stolyarov, M.Yu.Kupriyanov
JETP Letters 124, issue 1 (2026)