Hyperuniform vortex patterns at the surface of type-II superconductors

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.

arXiv comment17 pages, 8 figures

References in corpus (22)

• The Flux-Line Lattice in Superconductors
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Elastic theory of flux lattices in presence of weak disorder
• Designer disordered materials with large complete photonic band gaps
• Hyperuniform States of Matter
• Vortex-glass phases in type-II superconductors
• Inverse melting of the vortex lattice
• Moving glass theory of driven lattices with disorder
• Nonequilibrium Steady States of Driven Periodic Media
• A Bragg glass phase in the vortex lattice of a type II superconductor
• Driven Dynamics of Periodic Elastic Media in Disorder
• Non-equilibrium relaxation of an elastic string in a random potential
• First order phase transition from the vortex liquid to an amorphous solid
• Enhanced Pinning For Vortices in Hyperuniform Substrates and Emergent Hyperuniform Vortex States
• Glass phase of two-dimensional triangular elastic lattices with disorder
• Targeted evolution of pinning landscapes for large superconducting critical currents
• Structure of Flux Line Lattices with Weak Disorder at Large Length Scales
• Kinetic Theory of Flux Line Hydrodynamics:LIQUID Phase with Disorder
• Size-induced depression of first-order transition lines and entropy-jump in extremely-layered nanocrystalline vortex matter
• Persistence of the first-order transition lines in mesoscopic Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ vortex matter with less than hundred vortices
• Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor
• Excess of topological defects induced by confinement in vortex nanocrystals

Cited by in corpus (18)

• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Disordered hyperuniform vortex matter with rhombic distortions in FeSe at low fields
• Disordered Hyperuniform Quasi-1D Materials
• Anisotropic suppression of hyperuniformity of elastic systems in media with planar disorder
• Disordered hyperuniformity in superconducting vortex lattices
• Non-equilibrium dynamic hyperuniform states
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
• Jamming, Fragility and Pinning Phenomena in Superconducting Vortex Systems
• Hyperuniformity in Type-II Superconductors with Point and Planar Defects
• Non-Gaussian tail in the force distribution: A hallmark of correlated disorder in the host media of elastic objects
• Finite-size effects in hyperuniform vortex matter
• Superluminal Correlations in Ensembles of Optical Phase Singularities
• Anti-hyperuniform diluted vortex matter induced by correlated disorder
• Germanium-based nearly hyperuniform nanoarchitectures by ion beam impact
• Spectral Leakage and Masking Effects in the Measurement of Hyperuniformity
• Topological Defects, Inherent Structures, and Hyperuniformity
• Hyperuniform patterns nucleated at low temperatures: Insight from vortex matter imaged in unprecedentedly large fields-of-view