We present the results of an experimental study of vortex dynamics in non-twinned $YBa_2Cu_3O_{6,87}$ crystal. It is found that critical currents $J_c$ and $J_{c,dyn}$, which correspond to the pinning force in the thermal creep and flux flow mode, respectively, non-monotonically vary with the magnetic field. However, the minimum in the $J_{c,dyn}(H)$ dependence is observed in higher fields, compared with the minimum position $H_{OD}$ in the $J_c(H)$ dependence. Considering that the field $H_{OD}$ corresponds to the static order-disorder transition, this difference is explained by partial dynamic ordering of the vortex solid. It is concluded that finite transverse barriers guarantee finite density of transverse displacements of vortex lines $u_t\simeq c_La_0$ suitable for preservation of the disordered state of the moving vortex solid.
The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density jc at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to "weak collective pinning" and a magnetic field-independent …
The three-dimensional frustrated anisotropic XY model with point disorder is studied with both Monte Carlo simulations and resistively-shunted-junction dynamics to model the dynamics of a type-II superconductor with quenched point pinning in a magnetic field and a weak applied current. Both the collective pinning and the depinning of the Bragg glass is examined. We find a critical current I_c that separates a creep region with unmeasurable low voltage from a region with a voltage V \sim I-I_c, and also identify the mechanism behind this behavior. It is further found to be possible to collapse …
The upper critical field and flux pinning in MgB2 single crystals were investigated. The implications of these properties for technical applications are discussed and compared with transport properties of polycrystalline bulk samples and wires. In these untextured materials current percolation is important, especially at high magnetic fields. It is shown that the anisotropy of the upper critical field influences the "irreversibility line" and that the application range of MgB2 is limited by the smallest upper critical field (i.e., for the field direction perpendicular to the boron planes). Dis…
Explicit current-dependent expressions for anisotropic longitudinal and transverse nonlinear magnetoresistivities are represented and analyzed on the basis of a Fokker-Planck approach for two-dimensional single-vortex dynamics in a washboard pinning potential in the presence of point-like disorder. Graphical analysis of the resistive responses is presented both in the current-angle coordinates and in the rotating current scheme. The model describes nonlinear anisotropy effects caused by the competition of point-like (isotropic) and anisotropic pinning. Nonlinear guiding effects are discussed a…
We report significant alteration of the equilibrium properties of the superconductor HgBa$_2$Ca$_2$Cu$_3$O$_x$ when correlated disorder in the form of randomly oriented columnar tracks is introduced via induced fission of Hg-nuclei. From studies of the equilibrium magnetization $M_{eq}$ and the persistent current density over a wide range of temperatures, applied magnetic fields, and track densities up to a ``matching field'' of 3.4 Tesla, we observe that the addition of more columnar tracks acting as pinning centers is progressively offset by reductions in the magnitude of $M_{eq}$. Invoking …
We investigate the influence of disorders in terminal ethylene groups of BEDT-TTF molecules (ethylene-disorders) on the vortex pinning of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br. Magnetization measurements are performed under different cooling-processes. The second peak in the magnetization hysteresis curve is observed for all samples studied, and the hysteresis width of the magnetization becomes narrower by cooling faster. In contradiction to the simple pinning effect of disorder, this result shows the suppression of the vortex pinning force by introducing more ethylene-d…
We studied thermal and dynamic history effects in the vortex lattice (VL) near the order-disorder transition in clean NbSe$_2$ single crystals. Comparing the evolution of the effective vortex pinning and the bulk VL structure, we observed metastable superheated and supercooled VL configurations that coexist with a hysteretic effective pinning response due to thermal cycling of the system. A novel scenario, governed by the interplay between (lower) elastic and (higher) plastic energy barriers, is proposed as an explanation for our observations: Plastic barriers, which prevent the annihilation o…
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…
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…
The vortex lattice is an ideal system to study the competition and interplay between interaction and disorder. New results on 2H-NbSe_2 (in samples of progressively increasing pinning) elucidate how pinning alters the phase boundary separating the "ordered" and "disordered" states of the flux lines and causes a novel disorder-induced transition. A generic magnetic phase diagram of a type II superconductor.
We have performed a comparative study of two thin films of magnesium diboride (MgB2) grown by different techniques. The critical current density at different temperatures and magnetic fields was evaluated from magnetisation curves, the structure of superconducting order parameter was obtained from point-contact spectroscopy, and the scattering rates were evaluated by fitting the temperature dependent normal-state resistivity to the two-band model. The films have similar critical temperatures close to 39 K, but the upper critical fields were different by a factor of 2 (5.2T and 2.5 T at 20 K). …
The interrelation between heterogeneity and flux pinning is studied in Ba(Fe1-xCox)2As2 single crystals with widely varying Co-content x. Magnetic Bitter decoration of the superconducting vortex ensemble in crystals with x = 0:075 and x = 0:1 reveal highly disordered vortex structures. The width of the Meissner belt observed at the edges of the crystals, and above the surface steps formed by cleaving, as well as the width of the intervortex distance distribution, indicate that the observed vortex ensemble is established at a temperature just below the critical temperature Tc. The vortex intera…
We simulate the ordering of vortices and its effects on the critical current in superconductors with varied vortex-vortex interaction strength and varied pinning strengths for a two-dimensional system. For strong pinning the vortex lattice is always disordered and the critical depinning force only weakly increases with decreasing vortex-vortex interactions. For weak pinning the vortex lattice is defect free until the vortex-vortex interactions have been reduced to a low value, when defects begin to appear with a simultaneous rapid increase in the critical depinning force. In each case the depi…
A general phenomenology for phase behaviour in the mixed phase of type-II superconductors with weak point pinning disorder is outlined. We propose that the ``Bragg glass'' phase generically transforms via two separate thermodynamic phase transitions into a disordered liquid on increasing the temperature. The first transition is into a glassy phase, topologically disordered at the largest length scales; current evidence suggests that it lacks the long-ranged phase correlations expected of a ``vortex glass''. This phase has a significant degree of short-ranged translational order, unlike the dis…
The diversity of vortex melting and solid-solid transition lines measured in different high-T$_{c}$ superconductors is explained, postulating a unified order-disorder phase transition driven by both thermally- and disorder-induced fluctuations. The temperature dependence of the transition line and the nature of the disordered phase (solid, liquid, or pinned liquid) are determined by the relative contributions of these fluctuations and by the pinning mechanism. By varying the pinning mechanism and the pinning strength one obtains a spectrum of monotonic and non-monotonic transition lines simila…
We present a comprehensive overview of vortex pinning in single crystals of the isovalently substituted iron-based superconductor BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$, a material that qualifies as an archetypical clean superconductor, containing only sparse strong point-like pins [in the sense of C.J. van der Beek {\em et al.}, Phys. Rev. B {\bf 66}, 024523 (2002)]. Widely varying critical current values for nominally similar compositions show that flux pinning is of extrinsic origin. Vortex configurations, imaged using the Bitter decoration method, show less density fluctuations than those pre…
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…
We study theoretically the effects of heating on the magnetic flux moving in superconductors with a periodic array of pinning sites (PAPS). The voltage-current characteristic (VI-curve) of superconductors with a PAPS includes a region with negative differential resistivity (NDR) of S-type (i.e., S-shaped VI-curve), while the heating of the superconductor by moving flux lines produces NDR of N-type (i.e., with an N-shaped VI-curve). We analyze the instability of the uniform flux flow corresponding to different parts of the VI-curve with NDR. Especially, we focus on the appearance of the filamen…
We study the general problem of a manifold of interacting elastic lines whose spatial correlations are strongly affected by the competition between random and ordered pinning. This is done through magneto-transport experiments with YBa2Cu3O7-d thin films that contain a periodic vortex pinning array created via masked ion irradiation, in addition to the native random pinning. The strong field-matching effects we observe suggest the prevalence of periodic pinning, and indicate that at the matching field each vortex line is bound to an artificial pinning site. However, the vortex-glass transition…
Explorations of the order-disorder transformation in vortex matter in single crystals of tetragonal structured (c/a $\sim$3) borocarbide superconductors, $YNi_2B_2C$ and $LuNi_2B_2C$, reveal that vortex arrays experience different effective pinning in different crystallographic directions. We surmise that correlation exists between the large anisotropy in effective pinning/disorder and the differences in the (local) symmetry transition from rhombohedral to (quasi) square vortex lattice(VL). For field along high symmetry directions, like, c-axis and ab-basal plane, the VL symmetry is close to s…
We study theoretically the simultaneous effect of a regular and a random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing i…
We show numerically that in a binary system of Yukawa particles, a dispersity driven disordering transition occurs. In the presence of quenched disorder this disordering transition coincides with a marked increase in the depinning threshold, known as a peak effect. We find that the addition of poorly pinned particles can increase the overall pinning in the sample by increasing the amount of topological disorder present. If the quenched disorder is strong enough to create a significant amount of topological disorder in the monodisperse system, addition of a poorly pinned species generates furth…
In a sandwich consisting of two superconducting films, one weakly pinning and one strongly pinning, the vortex positions in both films are determined by the strongly pinning material and the vortex lattice is disordered in both films. We used (strongly pinning) NbN and (weakly pinning) MoGe and studied, by directly imaging the vortex core positions with a scanning tunnelling microscope, how this disorder is restored with increasing thickness of MoGe layer or when the interface is made insulating. For clean interfaces we find that the first reordering of the vortex lattice is found at a layer t…
Disorder induced melting, where the increase in positional entropy created by random pinning sites drives the order-disorder transition in a periodic solid, provides an alternate route to the more conventional thermal melting. Here, using real space imaging of the vortex lattice through scanning tunneling spectroscopy, we show that in the presence of weak pinning, the vortex lattice in a type II superconductor disorders through two distinct topological transitions. Across each transition, we separately identify metastable states formed through superheating of the low temperature state or super…
Destruction of the vortex lattice by random point pinning is considered as a mechanism of the ``second peak'' transition observed experimentally in weakly coupled layered high temperature superconductors. The transition field separating the topologically ordered quasilattice from the amorphous vortex configuration is strongly influenced by the layered structure and by the nonlocal nature of the vortex tilt energy due to the magnetic interlayer coupling. We found three different regimes of transition depending on the relative strength of the Josephson and magnetic couplings. The regimes can be …
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 study vortex pinning in layered type-II superconductors in the presence of uncorrelated disorder for decoupled layers. Introducing the new concept of variable-range thermal smoothing, we describe the interplay between strong pinning and thermal fluctuations. We discuss the appearance and analyze the evolution in temperature of two distinct non-linear features in the current-voltage characteristics. We show how the combination of layering and electromagnetic interactions leads to a sharp jump in the critical current for the onset of glassy response as a function of temperature.
We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different me…
The disordered flux line lattice in single crystals of the slightly overdoped aFe_{2-x}Co_xAs_2 (x = 0.19, Tc = 23 K) superconductor is studied by magnetization measurements, small-angle neutron scattering (SANS), and magnetic force microscopy (MFM). In the whole range of magnetic fields up to 9 T, vortex pinning precludes the formation of an ordered Abrikosov lattice. Instead, a vitreous vortex phase (vortex glass) with a short-range hexagonal order is observed. Statistical processing of MFM datasets lets us directly measure its radial and angular distribution functions and extract the radial…
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, longrange vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the RMS current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are consistent with those of the pure three-dimensional XY model.
We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe$_2$ and CeRu$_2$ with varying degree of random pinning. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomena, viz., the second magnetization peak (SMP) anomaly prior to the PE. Interplay between the path d…
Recent experiments show that charge-density-wave correlations are prevalent in underdoped cuprate superconductors. The correlations are short ranged at weak magnetic fields but their intensity and spatial extent increase rapidly at low temperatures beyond a crossover field. Here we consider the possibility of long-range charge-density-wave order in a model of a layered system where such order competes with superconductivity.We show that in the clean limit, low-temperature long-range order is stabilized by arbitrarily weak magnetic fields. This apparent discrepancy with the experiments is resol…
The statics and dynamics of magnetic flux quanta (fluxons) in long annular Josephson tunnel junctions have been investigated. Pinning by interaction of the fluxon field outside the junction with the superconducting wiring has been observed in spatially resolving measurements using low-temperature scanning electron microscopy. We were able to influence the characteristics of this field by carefully modifying the beam-induced fluxon trapping procedure. In this way we were able to select the pinning site acting on the fluxon.
The dynamics of vortices in a type-II superconductor with defects are studied by solving the time-dependent Ginzburg-Landau equations in two and three dimensions. We show that vortex flux tubes are trapped by volume defects up to a critical current density where they begin to jump between pinning sites along static flow channels. We study the dependence of the critical current on the pinning distribution and find for random distributions a maximum critical current equal to a few percent of the depairing current at a pinning density three times larger than the vortex line density. Whereas for a…
We report on the isotropic pinning obtained in epitaxial Fe(Se,Te) thin films grown on CaF2 (001) substrate. High critical current density values larger than 1 MA/cm2 in self field in liquid helium are reached together with a very weak dependence on the magnetic field and a complete isotropy. Analysis through Transmission Electron Microscopy evidences the presence of defects looking like lattice disorder at a very small scale, between 5 and 20 nm, which are thought to be responsible for such isotropic behavior in contrast to what observed on SrTiO3, where defects parallel to the c-axis enhance…
We examine the effects of disorder on striped phases in high-temperature superconductors and related materials. In the presence of quenched disorder, pinning by the atomic lattice - which might give rise to commensuration effects - is irrelevant for the stripe array on large length scales. As a consequence, the stripes have divergent displacement fluctuations and topological defects are present at all temperatures. Therefore the positional order of the stripe array is short ranged, with a finite correlation length even at zero temperature. Thus lock-in phenomena can exist only as crossovers bu…
It is demonstrated through Monte Carlo simulations that the one component lattice Coulomb gas model in two dimensions under certain conditions display features of an anomalous dynamic response. We suggest that pinning, which can either be due to the underlying discrete lattice or induced by disorder, is an essential ingredient behind this anomalous behavior. The results are discussed in relation to other situations where this response type appears, in particular the two components neutral Coulomb gas below the Kosterlitz-Thouless transition, as well as in relation to other findings from theory…
Material defects in hard type II superconductors pin the flux lines and thus establish the dissipation-free current transport in the presence of a finite magnetic field. Depending on the density and pinning force of the defects and the vortex density, pinning is either weak-collective or strong. We analyze the weak- to strong pinning crossover of vortex matter in disordered superconductors and discuss the peak effect appearing naturally in this context.
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 …
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 carry out extensive Monte Carlo simulations of the three-dimensional (3D) uniformly frustrated XY model with uncorrelated randomly perturbed couplings, as a model for the equilibrium behavior of an extreme type-II superconductor with quenched uncorrelated random point vortex pinning, in the presence of a uniform applied magnetic field. We map out the resulting phase diagram as a function of temperature T and pinning strength p for a fixed value of the vortex line density. At low p we find a sharp first order vortex lattice melting phase boundary separating a vortex lattice from a vortex liq…
The superconducting and structural properties of S/F/S (Superconductor/Ferromagnet/Superconductor) heterostructures have been studied by means of microwave measurements (1-20 GHz) and x-ray absorption fine structure (XAFS) spectroscopy. Nb/PdNi/Nb trilayers have been studied as a function of F layer thicness. With respect to pure Nb, XAFS analysis shows that the heterostructures exhibit larger structural disorder in the S layers. Microwave measurements show evidence for a progressively weaker vortex pinning with increasing F thickness. However, no clear correlation is found with the local diso…
We study the elasticity, fluctuations and pinning of a putative spontaneous vortex solid in ferromagnetic superconductors. Using a rigorous thermodynamic argument, we show that in the idealized case of vanishing crystalline pinning anisotropy the long-wavelength tilt modulus of such a vortex solid vanishes identically, as guaranteed by the underlying rotational invariance. The vanishing of the tilt modulus means that, to lowest order, the associated tension elasticity is replaced by the softer, curvature elasticity. The effect of this is to make the spontaneous vortex solid qualitatively more …
We discuss pinning properties of MgB2 thin films grown by pulsed-laser deposition (PLD) and by electron-beam (EB) evaporation. Two mechanisms are identified that contribute most effectively to the pinning of vortices in randomly oriented films. The EB process produces low defected crystallites with small grain size providing enhanced pinning at grain boundaries without degradation of Tc. The PLD process produces films with structural disorder on a scale less that the coherence length that further improves pinning, but also depresses Tc.
We investigate numerically the dynamically generated plastic deformations of a 3D vortex lattice (VL) driven through a disorder potential with isolated, strong pinning centers (point-like or extended along the field direction). We find that the VL exhibits a very peculiar dynamical behavior in the plastic flow regime, in particular, topological excitations consisting of three or four entangled vortices are formed. We determine the critical current density $j_c$ and the activation energy for depinning $U_c$ in the presence of a finite density of strong pinning centers.
We study, by means of three-dimensional Monte Carlo simulations, the current-voltage (IV) characteristics and the voltage noise spectrum at low temperatures of driven magnetic flux lines interacting with randomly placed point or columnar defects, as well as with periodically arranged linear pinning centers. Near the depinning current J_c, the voltage noise spectrum S(w) universally follows a 1/w^a power law. For currents J > J_c, distinct peaks appear in S(w) which are considerably more pronounced for extended as compared to point defects, and reflect the spatial distribution of the correlated…
In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice forms, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature $T_c$ increases with the applied …
Exotic vortex states with long range attraction and short range repulsion have recently been proposed to arise in superconducting hybrid structures and multi-band superconductors. Using large scale simulations we examine the static and dynamic properties of such vortex states interacting with random and periodic pinning. In the absence of pinning this system does not form patterns but instead completely phase separates. When pinning is present there is a transition from inhomogeneous to homogeneous vortex configurations similar to a wetting phenomenon. Under an applied drive, a dynamical dewet…
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…
We investigate the order - disorder transition line from a Bragg glass to an amorphous vortex glass in the H-T phase diagram of three-dimensional type-II superconductors with account of both pinning-caused and thermal fluctuations of the vortex lattice. Our approach is based on the Lindemann criterion and on results of the collective pinning theory and generalizes previous work of other authors. It is shown that the shapes of the order - disorder transition line and the vortex lattice melting curve are determined only by the Ginzburg number, which characterizes thermal fluctuations, and by a p…
Multi-quanta, or giant, vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for the formation of GVs. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.
