Hyperuniform vortex patterns at the surface of type-II superconductors

Abstract

A many-particle system must possess long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-z cross section. In this case, density fluctuations vanish isotropically as ∼q^{α} at small wave vectors q, with α=1. This prediction includes the solid and liquid vortex phases in the ideal clean case and the liquid in presence of weak uncorrelated disorder. We also show that the three-dimensional Bragg glass phase is marginally hyperuniform, while the Bose glass and the liquid phase with correlated disorder are expected to be nonhyperuniform at equilibrium. Furthermore, we compare these predictions with experimental results on the large-wavelength vortex density fluctuations of magnetically decorated vortex structures nucleated in pristine, electron-irradiated, and heavy-ion-irradiated superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} samples in the mixed state. For most cases, we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent α_{eff}≈1. We interpret these results in terms of a large-scale memory of the high-temperature line-liquid phase retained in the glassy dynamics when field cooling the vortex structures into the solid phase. We also discuss the crossovers expected from the dispersivity of the elastic constants at intermediate length-scales, and the lack of hyperuniformity in the x-y plane for lengths q^{−1} larger than the sample thickness due to finite-size effects in the z direction. We argue these predictions may be observable and propose further imaging experiments to test them independently.