Disordered hyperuniformity in superconducting vortex lattices
Jose Benito-Llorens, Isabel Guillamón, Ismael García-Serrano, Rosa Córdoba, Javier Sesé, José María De Teresa, M. Ricardo Ibarra, Sebastián Vieira, Miguel Ortuño, Hermann Suderow
Particles occupying sites of a random lattice present density fluctuations at all length scales. It has been proposed that increasing interparticle interactions reduces long range density fluctuations, deviating from random behaviour. This leads to power laws in the structure factor and the number variance that can be used to characterize deviations from randomness which eventually lead to disordered hyperuniformity. It is not yet fully clear how to link density fluctuations with interactions in a disordered hyperuniform system. Interactions between superconducting vortices are very sensitive to vortex pinning, to the crystal structure of the superconductor and to the value of the magnetic field. This creates lattices with different degrees of disorder. Here we study disordered vortex lattices in several superconducting compounds (Co-doped NbSe$_2$, LiFeAs and CaKFe$_4$As$_4$) and in two amorphous W-based thin films, one with strong nanostructured pinning (W-film-1) and another one with weak or nearly absent pinning (W-film-2). 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 indeed correlated to the presence of interactions. Furthermore, we find that we can describe all studied vortex lattices within a single framework consisting of a continous deviation from hyperuniformity towards random distributions when increasing the strength of pinning with respect to the intervortex interaction.
Disordered hyperuniform materials with vanishing long-wavelength density fluctuations are attracting attention due to their unique physical properties. In these systems, the large-scale density fluctuations are strongly suppressed as in a perfect crystal, even though the system can be disordered like a liquid. Yet, hyperuniformity can be affected by the different types of quenched disorder unavoidably present in the host medium where constituents are nucleated. Here, we use vortex matter in superconductors as a model elastic system to study how planar correlated disorder impacts the otherwise …
Disordered hyperuniformity is a state of matter which has isotropic liquid like properties while simultaneously having crystalline like properties such as little variation in the density fluctuations over long distances. Such states arise for the packing of photoreceptor cells in chicken eyes, jammed particle assemblies, and in nonequilibrium systems. An open question is what possible applications could utilize properties of hyperuniformity. One of the major issues for applications of type-II superconductors is how to achieve high critical currents by preventing the motion or depinning of vort…
We discuss the use of Langevin molecular dynamics in the investigation of the non-equilibrium properties of disordered vortex matter. Our special focus is set on values of system parameters that are realistic for disordered high-$T_c$ superconductors such as YBCO. Using a discretized elastic line model, we study different aspects of vortices far from thermal equilibrium. On the one hand we investigate steady-state properties of driven magnetic flux lines in a disordered environment, namely the current-voltage characteristics, the gyration radius, and the pinning time statistics. On the other h…
In the current quest to synthesize hyperuniform materials with interesting applications, addressing the coupling of the objects composing the system to the physical properties of the host medium is crucial. With this aim we study a model system: vortices in the FeSe superconductor subject to a considerable magneto-elastic coupling with the host sample. We reveal that the low-field FeSe vortex structure is of the weakest hyperuniform type possibly due to the relevance of the anisotropic and long-ranged interaction term introduced by the magneto-elastic coupling. This work indicates that it is p…
We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power law distributions…
Supercooling of the disordered vortex lattice in Bi_2Sr_2CaCu_2O_8+d
在最佳掺杂的Bi $_{2}$ Sr $_{2}$ CaCu $_{2}$ O $_{8+δ}$单晶中，在涡旋晶格有序-无序转变附近的时间分辨局域感应测量表明，高场无序相可以被淬灭到低至转变场一半的场.在一个重要的领域范围内，涡系统的电动力学行为是由样品中的两相共存。我们解释的结果在高场相的过冷和可能的第一阶性质的有序-无序过渡的“第二峰”。
Finite-size and quenching effects on hyperuniform structures formed during cooling
Low Temperatures Lab, Centro Atómico Bariloche, CNEA（低温实验室，巴里洛切原子中心，阿根廷国家原子能委员会）；Instituto de Nanociencia y Nanotecnología, CONICET-CNEA, Nodo Bariloche（纳米科学与技术研究所，CONICET-CNEA，巴里洛切节点）；Instituto Balseiro, CNEA and Universidad Nacional de Cuyo（巴尔塞罗研究所，阿根廷国家原子能委员会和门多萨国立大学）
We study the effects of rapid temperature and magnetic field changes on the non-equilibrium relaxation dynamics of magnetic vortex lines in disordered type-II superconductors by employing an elastic line model and performing Langevin molecular dynamics simulations. In a previously equilibrated system, either the temperature is suddenly changed, or the magnetic field is instantaneously altered which is reflected in adding or removing flux lines to or from the system. The subsequent aging properties are investigated in samples with either randomly distributed point-like or extended columnar defe…
We report unusual jamming in driven ordered vortex flow in 2H-NbS2. Reinitiating movement in these jammed vortices with a higher driving force, and halting it thereafter once again with a reduction in drive, unfolds a critical behavior centered around the de-pinning threshold via divergences in the lifetimes of transient states, validating the predictions of a recent simulation study, which also pointed out a correspondence between plastic de-pinning in vortex matter and the notion of random organization proposed in the context of sheared colloids undergoing diffusive motion.
We report structural evidence of dynamic reorganization in vortex matter in clean NbSe$_2$ by joint small angle neutron scattering and ac-susceptibility measurements. The application of oscillatory forces in a transitional region near the order-disorder transition results in robust bulk vortex lattice configurations with an intermediate degree of disorder. These dynamically-originated configurations correlate with intermediate pinning responses previously observed, resolving a long standing debate regarding the origin of such responses.
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and experimentally in electron sheets, dusty plasmas, colloidal and other systems. Here I show the different stages of defect formation in the vortex lattice of a superconductor while it undergoes an order-disorder transition by presenting real-space images of the lattice from scanning tunneling spectroscopy. When the system evolves from the ordered to the disordered state, …
The vortex matter in bulk type-II superconductors serves as a prototype system for studying the random pinning problem in condensed matter physics. Since the vortex lattice is embedded in an atomic lattice, small angle neutron scattering (SANS) is the only technique that allows for direct structural studies. In traditional SANS methods, the scattering intensity is a measure of the structure factor averaged over the entire sample. Recent studies in vortex physics have shown that it is highly desirable to develop a SANS technique which is capable of resolving the spatial inhomogeneities in the b…
Disorder can have remarkably disparate consequences in superconductors, driving superconductor-insulator transitions in ultrathin films by localizing electron pairs and boosting the supercurrent carrying capacity of thick films by localizing vortices (magnetic flux lines). Though the electronic 3D-to-2D crossover at material thicknesses $d \sim ξ$ (coherence length) is well studied, a similarly consequential magnetic crossover at $d \sim L_c$ (pinning length) that should drastically alter material properties remains largely underexamined. According to collective pinning theory, vortex segments…
Recent scanning tunneling experiments on $Ca_{2-x}Na_xCuO_2Cl_2$ by Hanaguri et al. observe field-dependent quasiparticle interference effects which are sensitive to the sign of the d-wave order parameter. Their analysis of spatial fluctuations in the local density of states shows that there is a selective enhancement of quasiparticle scattering events that preserve the gap sign, and a selective depression of the quasiparticle scattering events that reverse the gap sign. We introduce a model which accounts for this phenomenon as a consequence of vortex pinning to impurities. Each pinned vortex…
We study the non-equilibrium relaxation kinetics of interacting magnetic flux lines in disordered type-II superconductors at low temperatures by means of a three-dimensional elastic line model and Monte Carlo simulations. Investigating the vortex density and height autocorrelation functions as well as the flux line mean-square displacement, we observe the emergence of glassy dynamics, caused by the competing effects of vortex pinning due to point defects and long-range repulsive interactions between the flux lines. Our systematic numerical study allows us to carefully disentangle the associate…
We propose a mechanism of coherent emission from driven vortices in stacked intrinsic Josephson junctions. In contrast to super-radiance, which occurs only for highly ordered vortex lattices, we predict resonant radiation emission from weakly correlated vortex arrays. Our analytical results for the THz wave intensity, resonance frequencies, and the dependence of THz emission power on dissipation are in good agreement with the ones obtained by recent simulations.
We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb$_{75}$Zr$_{25}$ alloy. We also report the careful investigation of the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature and field dependent resistivity in t…
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 $\sim q^α$ at small wave-vectors $q$, with $α=1$. This prediction includes the solid and liquid vortex phases in …
We investigate the influence of quantum fluctuations and weak disorder on the vortex dynamics in a two-dimensional superconducting Berezinskii-Kosterlitz-Thouless system. The temperature below which quantum fluctuations dominate the vortex creep is determined, and the transport in this quantum regime is described. The crossover from quantum to classical regime is discussed and the quantum correction to the classical current-voltage relation is determined. It is found that weak disorder can effectively reduce the critical current as compared to that in the clean system.
We report the first direct observation of a disordered vortex matter phase existing near the edge of a bulk type-II superconductor Nb using a novel position-sensitive neutron diffraction technique. This "edge-contaminated" vortex state was implicated in previous studies using transport techniques and was postulated to have played a significant role in the behavior of vortex dynamics in a wide range of type-II superconductors. It is found that upon thermal annealing, the vortex matter in the bulk undergoes re-ordering, suggesting that the edge-contaminated bulk vortex state is metastable. The e…
