Disordered hyperuniformity in superconducting vortex lattices

The current carrying capability of type II superconductors under magnetic fields is determined to a large extent by the interaction of superconducting vortices with pinning centers. Vortices are arranged in lattices with varying degrees of disorder depending on the balance between the intervortex interactions and the pinning strength. We analyze here vortex arrangements in disordered vortex lattices of different superconducting systems, single crystals (Co-doped NbSe2, LiFeAs, and CaKFe4As4), and amorphous W- based thin films (with critical temperatures T-c from 4 K to 35 K and critical fields from 3.4 T to more than 90 T). We calculate for each case the structure factor and number variance and compare to calculations on an interacting set of partially pinned particles. We find that random density fluctuations appear when pinning overcomes interactions and show that the suppression of density fluctuations is correlated to the presence of interactions. We discuss the results within the framework of hyperuniform distributions and find that all studied lattices follow a similar increase of the number variance with the defect density