# Spontaneous Pattern Formation in Intertype Superconducting Films

## TL;DR

This paper investigates the spontaneous formation of complex pattern structures in thin superconducting films within the intertype regime, revealing their independence from boundary conditions and their relation to the removal of degeneracy at the Bogomolnyi point.

## Contribution

It demonstrates that intertype superstructures in thin superconducting films are qualitatively unaffected by boundary conditions, linking their formation to degeneracy removal at the Bogomolnyi point.

## Key findings

- Superstructures are boundary-condition independent.
- Pattern formation is tied to the removal of degeneracy.
- Intertype regime exhibits complex, sensitive patterns.

## Abstract

Thin superconducting films are usually regarded as type II superconductors even when they are made of a type I material. The reason is a strong contribution of the stray magnetic field that stabilizes vortices. While very thin films indeed reach this limit, there is a large interval of film thicknesses where the magnetic properties cannot be classified as either of the two conventional superconductivity types. Recent calculations revealed that in this interval the system exhibits spontaneous formation of complex condensate-field patterns that are very sensitive to system parameters, in particular, the temperature and the applied magnetic field. The corresponding superconducting magnetic properties can be attributed to a special regime of the intertype superconductivity whose physical origin lies in the removal of an infinite degeneracy of the self-dual superconducting state at the critical Bogomolnyi point. Here we demonstrate that qualitative characteristics of the intertype superstructures in thin superconducting films are independent of the choice of the in-plane boundary conditions for the order parameter and the magnetic field.