Microscopic study of the intermediate mixed state in intertype superconductors

We present a comprehensive microscopic study of the intermediate mixed state in superconductors of the intertype (IT) regime separating types I and II. Using fully self-consistent Bogoliubov–de Gennes calculations for a lattice model, we analyze few-vortex configurations across the entire temperature range 0 < T < T c . Our results demonstrate the key features of IT superconductivity, namely, nonmonotonic vortex interactions and formation of vortex clusters. Using results of the calculations, we construct a “temperature–coupling” phase diagram that delineates distinct superconducting regimes and shows their convergence at a single Bogomolnyi point, consistent with earlier predictions of extended Ginzburg–Landau theory. Additionally, we identify a deep IT region of irregular vortex configurations apparently dominated by many-body vortex effects. The results establish a fully microscopic foundation for the IT superconductivity and extend its description beyond the vicinity of the critical temperature.