# Microscopic study of the intermediate mixed state in intertype superconductors

## TL;DR

This paper studies the intermediate mixed state in intertype superconductors using detailed calculations to reveal new insights into vortex behavior and phase transitions.

## Contribution

The study provides a microscopic foundation for intertype superconductivity and identifies a deep region of irregular vortex configurations.

## Key findings

- Nonmonotonic vortex interactions and vortex clusters are key features of intertype superconductivity.
- A temperature–coupling phase diagram is constructed, showing convergence at a Bogomolnyi point.
- A deep intertype region with irregular vortex configurations is identified, dominated by many-body effects.

## Abstract

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 < Tc. 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.