# Possible existence of a filamentary state in type-II superconductors

## TL;DR

This study provides evidence that in type-II superconductors, a filamentary superconducting phase persists above the upper critical field Hc2, challenging the traditional understanding of their phase diagram.

## Contribution

The paper presents experimental evidence of filamentary superconductivity above Hc2, suggesting a revision of the standard phase diagram for type-II superconductors.

## Key findings

- Superconducting phase exists above Hc2 in niobium samples.
- Hc3 is the same in parallel and perpendicular magnetic fields.
- Filaments form parallel to the magnetic field, maintaining a hexagonal structure.

## Abstract

The standard interpretation of the phase diagram of type-II superconductors was developed in 1960s and has since been considered a well-established part of classical superconductivity. However, upon closer examination a number of fundamental issues arise that leads one to question this standard picture. To address these issues we studied equilibrium properties of niobium samples near and above the upper critical field Hc2 in parallel and perpendicular magnetic fields. The samples investigated were very high quality films and single crystal discs with the Ginzburg-Landau parameters 0.8 and 1.3, respectively. A range of complementary measurements have been performed, which include dc magnetometry, electrical transport, muSR spectroscopy and scanning Hall-probe microscopy. Contrarily to the standard scenario, we observed that a superconducting phase is present in the sample bulk above Hc2 and the field Hc3 is the same in both parallel and perpendicular fields. Our findings suggest that above Hc2 the superconducting phase forms filaments parallel to the field regardless on the field orientation. Near Hc2 the filaments preserve the hexagonal structure of the preceding vortex lattice of the mixed state and the filament density continuously falls to zero at Hc3. Our work has important implications for the correct interpretation of properties of type-II superconductors and can also be essential for practical applications of these materials.