Hyperuniform vortex patterns at the surface of type-II superconductors

Gonzalo Rumi,Yanina Fasano,Jazmín Aragón Sánchez,Federico Elías,Joaquín Puig,Alejandro B Kolton,Gladys Nieva,Raúl Cortés Maldonado,Néstor René Cejas Bolecek,Marcin Konczykowski

doi:10.1103/physrevresearch.1.033057

Abstract

A many-particle system must posses 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 $\sim q^{\alpha}$ at small wave-vectors $q$, with $\alpha=1$. 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 non-hyperuniform 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 BiSCCO samples in the mixed state. For most cases we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent $\alpha_{\text{eff}} \approx 1$. 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.

Highlights

Hyperuniform point patterns, defined by a complete suppression of density fluctuations in the large-wavelength limit [1], have attracted great interest in recent years
We 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
We show that by adding heuristic arguments these assertions can be extended to predict the density fluctuations in the Bragg glass, Bose glass, and liquid vortex phases with correlated disorder generated by columnar defects (CD)

Summary

Introduction

Hyperuniform point patterns, defined by a complete suppression of density fluctuations in the large-wavelength limit [1], have attracted great interest in recent years. Such behavior can spontaneously emerge, following either equilibrium or nonequilibrium protocols, in disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, photoreceptor cells, and even the immune system [1,2,3]. Hyperuniform systems are proposed to be distinguishable states of matter characterized by special properties [2] These properties can be technologically exploited directly, or indirectly, by coupling a given system with a hyperuniform pattern. The fabrication of such patterns, either in a controlled or a self-assembled way, is of interest from an applied point of view [3].

Results

Discussion

Conclusion