Vortices In type-II Superconductors Research Articles

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mox\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{x}$$\\end{document}Ge1-x\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{1-x}$$\\end{document} film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

Surface barrier effect as evidence of chiral soliton lattice formation in chiral dichalcogenide CrTa3S6 crystals

The formation of chiral magnetic soliton lattice (CSL) is investigated in monoaxial chiral dichalcogenide CrTa3S6 crystals in terms of a surface barrier, which prevents the penetration of chiral solitons into the system and is an intrinsic origin of hysteresis for the continuous phase transition of nucleation-type, as discussed in the system of quantized vortices in type-II superconductors. The magnetoresistance (MR) was examined with microfabricated platelet samples in different dimensions with regard to the c-axis direction of the crystal. The CSL formation was confirmed by the discrete MR changes, reflecting the number of chiral solitons, as well as by the presence of a surface barrier, recognized as a fixed ratio of critical magnetic fields during the hysteresis field cycle. We also argue the influence of the surface barrier in bulk CrTa3S6 crystals.

Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime

Systems consisting of confined, interacting particles doing overdamped motion admit an effective description in terms of nonlinear Fokker-Planck equations. The behavior of these systems is closely related to the S power-law entropies and can be interpreted in terms of the S-based thermostatistics. The connection between overdamped systems and the S measures provides valuable insights on diverse physical problems, such as the dynamics of interacting vortices in type-II superconductors. The S-thermostatistical approach to the study of many-body systems described by nonlinear Fokker-Planck equations has been intensively explored in recent years, but most of these efforts were restricted to systems affected by time-independent external potentials. Here, we extend this treatment to systems evolving under time-dependent external forces. We establish a lower bound on the work done by these forces when they drive the system during a transformation. The bound is expressed in terms of a free energy based on the S entropy and is satisfied even if the driving forces are not derivable from a potential function. It constitutes a generalization, for systems governed by nonlinear Fokker-Planck equations involving general time-dependent external forces, of the H-theorem satisfied by these systems when the external forces arise from a time-independent potential.

Motion of magnetic vortices in type-Ⅱ superconductor with randomly distributed pinning centers

The dynamic behaviors of the magnetic vortices in a two-dimensional square superconductor with randomly distributed pinning centers of normal state were considered using the Ginzburg-Landau (G-L) model. The pinning centers are randomly distributed as various contents in all the area of the superconductor and a distribution function p(r) defined in a MATLAB is used to determinate the size and sites of normal state pinning centers. Using COMSOL and MATLAB, we analyzed the magnetization curves and the density of superconducting electrons as a function of the external magnetic field applied along the z-axis. Simulation results showed that the vortices configurations and magnetization depend on the content of the pinning centers and the maximum magnetization values decrease exponentially as the content increases. The content of pinning centers with the largest mixed state is determined by modeling the number of the magnetic vortices trapped in the pinning centers. This work will provide good results into understanding the dynamics of the magnetic vortices in a superconductor with randomly distributed pinning centers in view of the circumstance that they are randomly distributed in the superconductor during fabricating it.

Active rheology and anticommensuration effects for driven probe particles on two-dimensional periodic pinning substrates

For an assembly of particles interacting with a two-dimensional periodic substrate, a series of commensuration effects can arise when the number of particles is an integer multiple of the number of substrate minima. Such commensuration effects can appear for vortices in type-II superconductors with periodic pinning or for colloidal particles on optical landscapes. Under bulk external driving, the pinning or drag on the particles is strongly enhanced at commensuration. Here we consider the active rheology of a single particle driven through an assembly of particles coupled to a periodic substrate at different commensurate conditions. For increasing density at fixed driving force, we observe nonmonotonic drag along with what we call an anticommensuration effect where the drag or pinning effectiveness is reduced in commensurate states, opposite from the behavior typically observed under bulk driving. The velocity enhancement or drag reduction appears when the background particles form a crystalline state that is coupled more strongly to the substrate than to the driven particle, while under incommensurate conditions, the background particles are disordered and produce enhanced drag on the probe particle. The velocity noise of the driven particle has a narrow band signature at commensuration and a broad band signature away from commensuration. We map out the regions in which viscous flow, periodic flow, and a pinned phase appear. We show that the effects we observe are robust on both square and triangular substrate arrays and for both vortices in type-II superconductors and colloidal particles on optical landscapes.

Motion of Magnetic Vortices in Type-Ii Superconductor with Randomly Distributed Pinning Centers

Motion of Magnetic Vortices in Type-Ii Superconductor with Randomly Distributed Pinning Centers

Defects in conformal crystals: Discrete versus continuous disclination models

We study the relationship between topological defect formation and ground-state 2D packings in a model of repulsions in external confining potentials. Specifically we consider screened 2D Coulombic repulsions, which conveniently parameterizes the effects of interaction range, but also serves as simple physical model of confined, parallel arrays of polyelectrolyte filaments or vortices in type II superconductors. The countervailing tendencies of repulsions and confinement to, respectively, spread and concentrate particle density leads to an energetic preference for nonuniform densities in the clusters. Ground states in such systems have previously been modeled as conformal crystals, which are composed of locally equitriangular packings whose local areal densities exhibit long-range gradients. Here we assess two theoretical models that connect the preference for nonuniform density to the formation of disclination defects, one of which assumes a continuum distributions of defects, while the second considers the quantized and localized nature of disclinations in hexagonal conformal crystals. Comparing both theoretical descriptions to numerical simulations of discrete particles clusters, we study the influence of interaction range and confining potential on the topological charge, number, and distribution of defects in ground states. We show that treating disclinations as continuously distributable well captures the number of topological defects in the ground state in the regime of long-range interactions, while as interactions become shorter range, it dramatically overpredicts the growth in total defect charge. Detailed analysis of the discretized defect theory suggests that that failure of the continuous defect theory in this limit can be attributed to the asymmetry in the preferred placement of positive vs negative disclinations in the conformal crystal ground states, as well as a strongly asymmetric dependence of self-energy of disclinations on sign of topological charge.

Spin Hall effect generated by fluctuating vortices in type-II superconductors

We theoretically investigate the vortex spin Hall effect, i.e., a novel spin Hall effect driven by the motion of superconducting vortices, by focusing on the role of superconducting fluctuations. Within the BCS-Gor'kov microscopic approach combined with the Kubo formula, we find a strong similarity between the vortex spin Hall effect and the vortex Nernst/Ettingshausen effect. Calculated temperature dependence of the voltage signal due to the inverse vortex spin Hall effect exhibits a strong enhancement by vortex fluctuations. This result not only provides a possible explanation for a prominent peak found in the spin Seebeck effect in a NbN/Y$_3$Fe$_5$O$_{12}$ system, but also leads to a proposal of new experiments using other superconductors with strong fluctuations, such as cuprate or iron-based superconductors.

Interaction between moving Abrikosov vortices in type-II superconductors

The self-energy of a moving vortex is shown do decrease with increasing velocity. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term $\propto v^2$; the "slow" motion is defined as having the velocity $v<v_c =c^2/4\pi\sigma\lambda$, where $\sigma (T)$ is conductivity of the normal excitations and $\lambda (T)$ is London penetration depth. For higher velocities, $v>v_c(T)$, the interaction energy of two vortices situated along the velocity direction is enhanced and along the perpendicular direction is suppressed compared to the static case.

Thermostatistics of overdamped motion with anisotropic drag forces

We investigate the consequences of anisotropic drag forces for the thermostatistics of systems of interacting particles in the overdamped motion regime. Systems of confined particles interacting via short-range forces and performing overdamped motion exhibit interesting thermodynamic features, and constitute useful models for various problems in physics and other areas. In particular, they proved useful for the study of interacting vortices in type-II superconductors. The dynamics of the above mentioned many-particle systems admits an effective description based on nonlinear Fokker-Planck equations with power-law diffusion terms. Most works studying this kind of systems, and their relationship with nonlinear Fokker-Planck equations, assume isotropic drag forces. In the present work we consider the effects of anisotropic drag forces on this kind of systems. We derive the corresponding nonlinear Fokker-Planck equations and investigate some of their main properties.

Deformation of the moving magnetic skyrmion lattice in MnSi under electric current flow

Topological defects are found ubiquitously in various kinds of matter, such as vortices in type-II superconductors, and magnetic skyrmions in chiral ferromagnets. While knowledge on the static behavior of magnetic skyrmions is accumulating steadily, their dynamics under forced flow is still a widely open issue. Here, we report the deformation of the moving magnetic skyrmion lattice in MnSi under electric current flow observed using small-angle neutron scattering. A spatially inhomogeneous rotation of the skyrmion lattice, with an inverse rotation sense for opposite sample edges, is observed for current densities greater than a threshold value jt ~ 1 MA m−2 (106 A m−2). Our result show that skyrmion lattices under current flow experience significant friction near the sample edges due to pinning, this being a critical effect that must be considered for anticipated skyrmion-based applications at the nanoscale.

Charging in a Superconducting Vortex Due to the Three Force Terms in Augmented Eilenberger Equations

We derive augmented Eilenberger equations that incorporate the following missing force terms: (i) the Lorentz force, (ii) the pair-potential gradient (PPG) force, and (iii) the pressure difference arising from the slope in the density of states (DOS). Recently, augmented Eilenberger equations with the Lorentz and PPG forces have been derived microscopically by studying the Hall and charging effects in superconductors, but the pressure due to the slope in the DOS has not yet been considered in augmented Eilenberger equations, despite phenomenological indications that it is a charging mechanism in a vortex of type-II superconductors. This newly added pressure is called "the SDOS pressure". We calculate the charging in an isolated vortex of an s-wave superconductor with a spherical Fermi surface using the augmented Eilenberger equations incorporating the Lorentz force, PPG force, and SDOS pressure. When we compare the charge densities due to the three force terms in the augmented Eilenberger equations, the vortex-core charging due to the SDOS pressure is larger than that due to the other forces near the superconducting transition temperature. Thus, when we calculate the charging in an isolated vortex of a superconductor with a finite slope in the DOS, we should consider not only the Lorentz and PPG forces but also the SDOS pressure.

Structural transitions in vortex systems with anisotropic interactions

We introduce a model of vortices in type-II superconductors with a four-fold anisotropy in the vortex–vortex interaction potential. Using numerical simulations we show that the vortex lattice undergoes structural transitions as the anisotropy is increased, with a triangular lattice at low anisotropy, a rhombic intermediate state, and a square lattice for high anisotropy. In some cases we observe a multi-q state consisting of an Archimedean tiling that combines square and triangular local ordering. At very high anisotropy, domains of vortex chain states appear. We discuss how this model can be generalized to higher order anisotropy as well as its applicability to other particle-based systems with anisotropic particle–particle interactions.

Parallel magnetic field suppresses dissipation in superconducting nanostrips

The motion of Abrikosov vortices in type-II superconductors results in a finite resistance in the presence of an applied electric current. Elimination or reduction of the resistance via immobilization of vortices is the "holy grail" of superconductivity research. Common wisdom dictates that an increase in the magnetic field escalates the loss of energy since the number of vortices increases. Here we show that this is no longer true if the magnetic field and the current are applied parallel to each other. Our experimental studies on the resistive behavior of a superconducting Mo0.79Ge0.21 nanostrip reveal the emergence of a dissipative state with increasing magnetic field, followed by a pronounced resistance drop, signifying a reentrance to the superconducting state. Large-scale simulations of the 3D time-dependent Ginzburg-Landau model indicate that the intermediate resistive state is due to an unwinding of twisted vortices. When the magnetic field increases, this instability is suppressed due to a better accommodation of the vortex lattice to the pinning configuration. Our findings show that magnetic field and geometrical confinement can suppress the dissipation induced by vortex motion and thus radically improve the performance of superconducting materials.

Thermodynamic framework for compact q-Gaussian distributions

Recent works have associated systems of particles, characterized by short-range repulsive interactions and evolving under overdamped motion, to a nonlinear Fokker–Planck equation within the class of nonextensive statistical mechanics, with a nonlinear diffusion contribution whose exponent is given by ν=2−q. The particular case ν=2 applies to interacting vortices in type-II superconductors, whereas ν>2 covers systems of particles characterized by short-range power-law interactions, where correlations among particles are taken into account. In the former case, several studies presented a consistent thermodynamic framework based on the definition of an effective temperature θ (presenting experimental values much higher than typical room temperatures T, so that thermal noise could be neglected), conjugated to a generalized entropy sν (with ν=2). Herein, the whole thermodynamic scheme is revisited and extended to systems of particles interacting repulsively, through short-ranged potentials, described by an entropy sν, with ν>1, covering the ν=2 (vortices in type-II superconductors) and ν>2 (short-range power-law interactions) physical examples. One basic requirement concerns a cutoff in the equilibrium distribution Peq(x), approached due to a confining external harmonic potential, ϕ(x)=αx2∕2 (α>0). The main results achieved are: (a) The definition of an effective temperature θ conjugated to the entropy sν; (b) The construction of a Carnot cycle, whose efficiency is shown to be η=1−(θ2∕θ1), where θ1 and θ2 are the effective temperatures associated with two isothermal transformations, with θ1>θ2; (c) Thermodynamic potentials, Maxwell relations, and response functions. The present thermodynamic framework, for a system of interacting particles under the above-mentioned conditions, and associated to an entropy sν, with ν>1, certainly enlarges the possibility of experimental verifications.

Charging due to Pair-Potential Gradient in Vortex of Type-II Superconductors

Besides the magnetic Lorentz force familiar from the Hall effect in metals and semiconductors, there exists a mechanism for charging peculiar to superconductors that is caused by the pair-potential gradient (PPG). We incorporate it in the augmented quasiclassical equations of superconductivity with the Lorentz force to study charging of an isolated vortex in an equilibrium s-wave type-II superconductor. It is found that the PPG mechanism gives rise to charging concentrated within the core whose magnitude at the core center can be 10 to 100 times larger than that caused by the Lorentz force. Our detailed calculations on the spatial, temperature, and magnetic-penetration-depth dependences of the vortex-core charge reveal that the PPG mechanism contributes dominantly to the core charging of the isolated vortex over a wide parameter range. The two mechanisms are also found to work additively at the core center for the present model with an isotropic Fermi surface.

Reversible ratchet effects for vortices in conformal pinning arrays

A conformal transformation of a uniform triangular pinning array produces a structure called a conformal crystal which preserves the six-fold ordering of the original lattice but contains a gradient in the pinning density. Here we use numerical simulations to show that vortices in type-II superconductors driven with an ac drive over gradient pinning arrays produce the most pronounced ratchet effect over a wide range of parameters for a conformal array, while square gradient or random gradient arrays with equivalent pinning densities give reduced ratchet effects. In the conformal array, the larger spacing of the pinning sites in the direction transverse to the ac drive permits easy funneling of interstitial vortices for one driving direction, producing the enhanced ratchet effect. In the square array, the transverse spacing between pinning sites is uniform, giving no asymmetry in the funneling of the vortices as the driving direction switches, while in the random array, there are numerous easy-flow channels present for either direction of drive. We find multiple ratchet reversals in the conformal arrays as a function of vortex density and ac amplitude, and correlate the features with a reversal in the vortex ordering, which is greater for motion in the ratchet direction. The enhanced conformal pinning ratchet effect can also be realized for colloidal particles moving over a conformal array, indicating the general usefulness of conformal structures for controlling the motion of particles.

Comparing the dynamics of skyrmions and superconducting vortices

Vortices in type-II superconductors have attracted enormous attention as ideal systems in which to study nonequilibrium collective phenomena, since the self-ordering of the vortices competes with quenched disorder and thermal effects. Dynamic effects found in vortex systems include depinning, nonequilibrium phase transitions, creep, structural order–disorder transitions, and melting. Understanding vortex dynamics is also important for applications of superconductors which require the vortices either to remain pinned or to move in a controlled fashion. Recently, topological defects called skyrmions have been realized experimentally in chiral magnets. Here we highlight similarities and differences between skyrmion dynamics and vortex dynamics. Many of the previous ideas and experimental setups that have been applied to superconducting vortices can also be used to study skyrmions. We also discuss some of the differences between the two systems, such as the potentially large contribution of the Magnus force in the skyrmion system that can dramatically alter the dynamics and transport properties.

Aspects of jamming in two-dimensional athermal frictionless systems

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce jamming densities much lower than those observed for disk-shaped particles, and we show how jamming exhibits fragility for some shapes while for other shapes this is absent. Next we describe the effects of long range interactions and jamming behavior in systems such as charged colloids, vortices in type-II superconductors, and dislocations. We consider the effect of adding obstacles to frictionless jamming systems and discuss connections between this type of jamming and systems that exhibit depinning transitions. Finally, we discuss open questions such as whether the jamming transition in all these different systems can be described by the same or a small subset of universal behaviors, as well as future directions for studies of jamming transitions in two dimensional systems, such as jamming in self-driven or active matter systems.

Strongly Enhanced Pinning of Magnetic Vortices in Type-II Superconductors by Conformal Crystal Arrays

Conformal crystals are nonuniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of local ordering in the conformally transformed hexagonal lattice and the arching arrangement of the pinning also play crucial roles. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.