Universal flux patterns and their interchange in superconductors between types I and II

Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic flux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such configurations has not been presented. We solve this old-standing fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic configurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the self-duality of the theory that is universal and not sensitive to the microscopic details. Classification into type I and II reflects different responses of a superconductor to an applied magnetic field, however, there are intertype materials with unique properties and atypical vortex configurations. The authors study vortex patterns in this regime revealing that their properties are governed by a universal material independent mechanism, which amends the dual classification.