The coexistence of type-I and type-II superconductivity in mesoscopic single crystals

We show that the well established criteria for type-I to type-II transitions in bulk materials do not apply to mesoscopic superconductors, as the dual point depends both on the material properties and on temperature. In electrochemically formed triangular Pb single crystals, we even found the coexistence of both types of superconductivity -- while retaining Meissner behavior with increasing magnetic field all the way through the superheated phase, the sample can still capture vortices in the metastable regime. When the field is swept back, in realistic type-I structures with intrinsic pinning, the vortices can survive in the sample even when the field changes polarity, contrary to conventional behavior. All findings are substantiated by state-of-the-art 3D Ginzburg-Landau simulations and $\mu $-Hall probe measurements.