Vortex Lattice In Superconductors Research Articles

Anti-matching effect in a two dimensional driven vortex lattice in the presence of periodic pinning

The dynamics of a driven superconducting vortex lattice in a two-dimensional (2D) periodic potential of square symmetry is studied using Brownian dynamics simulations. The range and strength of the vortex-substrate interaction are taken to be of the same order as that of the vortex-vortex interaction. The matching effect in a driven vortex lattice in the presence of a periodic array of pinning centers refers to the enhanced resistance to the vortex lattice motion when the ratio of the number of vortices to the number of pinning centers (called the filling fraction) takes simple fractional values. In particular, one expects a pronounced matching effect when the filling fraction is one. Contrary to this expectation, a drop in the vortex lattice mobility is observed as the filling fraction is increased from value one. This anti-matching effect can be understood in terms of the structural change in the vortex lattice as the filling fraction is varied. The dip observed in vortex mobility as a function of temperature when the filling fraction equals one (Joseph T 2020PhysicaA556124737), is studied for other values of filling above and below one. The behavior is found to persist for other fillings as well and is associated with the melting of the vortex lattice. The temperature at which the lattice melts is found to increase with drive and explains the shift in the temperature at which mobility is a minimum, locally.

Is spontaneous vortex generation in superconducting 4Hb-TaS2 from vison-vortex nucleation with Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{Z}_{2}$\\end{document} topological order?

We propose the superconducting van der Waals material 4Hb-TaS2 to realize the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{Z}_{2}$\\end{document} topological order and interpret the recent discovery of the spontaneous vortex generation in 4Hb-TaS2 as the vison-vortex nucleation. For the alternating stacking of metallic/superconducting and Mott insulating layers in 4Hb-TaS2, we expect the local moments in the Mott insulating 1T-TaS2 layer to form the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{Z}_{2}$\\end{document} topological order. The spontaneous vortex generation in 4Hb-TaS2 is interpreted from the transition or nucleation between the superconducting vortex and the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{Z}_{2}$\\end{document} vison in different phase regimes. Differing from the single vison-vortex nucleation in the original Senthil–Fisher’s cuprate proposal, we consider such nucleation process between the superconducting vortex lattice and the vison crystal. We further propose experiments to distinguish this proposal with the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{Z}_{2}$\\end{document} topological order from the chiral spin liquid scenarios.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Transport signatures of fragile glass dynamics in the melting of the two-dimensional vortex lattice

In a two-dimensional superconducting vortex lattice, the melting from the solid to the isotropic liquid can occur via an intermediate phase that retains orientational correlations. The effect of such correlations on transport and their interplay with the quenched disorder remain open questions. We perform magnetotransport measurements in a wide range of temperatures and magnetic fields on a weakly pinned two-dimensional vortex system in amorphous MoGe films. While at high fields, where quenched disorder dominates, we recover the typical strong-glass behavior of a vortex liquid, at low fields the resistivity shows a clear crossover to a fragile vortex glass. Our findings, supported by numerical simulations, suggest that this is a signature of heterogeneous dynamics that arises from the presence of orientational correlations.

Field angle dependent vortex lattice phase diagram in MgB2

Using small-angle neutron scattering we have studied the superconducting vortex lattice (VL) phase diagram in MgB2 as the applied magnetic field is rotated away from the c axis and towards the basal plane. The field rotation gradually suppresses the intermediate VL phase which exists between end states aligned with two high symmetry directions in the hexagonal basal plane for H || c. Above a critical angle, the intermediate state disappears, and the previously continuous transition becomes discontinuous. The evolution towards the discontinuous transition can be parameterized by a vanishing twelvefold anisotropy term in the VL free energy.

Disordered hyperuniformity in superconducting vortex lattices

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.

Universal chiral magnetic effect in the vortex lattice of a Weyl superconductor

It was shown recently that Weyl fermions in a superconducting vortex lattice can condense into Landau levels. Here we study the chiral magnetic effect in the lowest Landau level: The appearance of an equilibrium current I along the lines of magnetic flux Φ, due to an imbalance between Weyl fermions of opposite chirality. A universal contribution dI∕dΦ=(e∕h)2μ (at equilibrium chemical potential μ relative to the Weyl point) appears when quasiparticles of one of the two chiralities are confined in vortex cores. The confined states are charge-neutral Majorana fermions.

Thermal creep induced by cooling a superconducting vortex lattice

A perturbed system relaxes towards an equilibrium given by a minimum in the potential energy landscape. This often occurs by thermally activated jumps over metastable states. The corresponding dynamics is named creep and follows Arrhenius' law. Here we consider the situation where the equilibrium position depends on temperature. We show that this effect occurs in the vortex lattice of the anisotropic superconductor $2\mathrm{H}$-$\mathrm{Nb}\mathrm{Se}_{2}$ when the magnetic field is tilted away from the principal axes, and that it leads to the peculiar appearance of creep when cooling the sample. Temperature determines the system's ground state and at the same time brings the system back to equilibrium, playing a dual and antagonistic role. We expect that cooling induced creep occurs in correlated systems with many degrees of freedom allowing to tune the equilibrium state via heat treatment.

Magnetic skyrmion lattice by the Fourier transform method

We demonstrate a fast numerical method of theoretical studies of skyrmion lattice or spiral order in magnetic materials with Dzyaloshinsky-Moriya interaction. The method is based on the Fourier expansion of the magnetization combined with a minimization of the free energy functional of the magnetic material in Fourier space, yielding the optimal configuration of the system for any given set of parameters. We employ a Lagrange multiplier technique in order to satisfy micromagnetic constraints. We apply this method to a system that exhibits, depending on the parameter choice, ferromagnetic, skyrmion lattice, or spiral (helical) order. Known critical fields corresponding to the helical-skyrmion as well as the skyrmion-ferromagnet phase transitions are reproduced with high precision. Using this numerical method we predict new types of excited (metastable) states of the skyrmion lattice, which may be stabilized by coupling the skyrmion lattice with a superconducting vortex lattice. The method can be readily adapted to other micromagnetic systems.

Structural transition kinetics and activated behavior in the superconducting vortex lattice

Using small-angle neutron scattering, we investigated the behavior of a metastable vortex lattice state in MgB2 as it is driven towards equilibrium by an AC magnetic field. This shows an activated behavior, where the AC field amplitude and cycle count are equivalent to, respectively, an effective "temperature" and "time". The activation barrier increases as the metastable state is suppressed, corresponding to an aging of the vortex lattice. Furthermore, we find a cross-over from a partial to a complete suppression of metastable domains depending on the AC field amplitude, which may empirically be described by a single free parameter. This represents a novel kind of collective vortex behavior, most likely governed by the nucleation and growth of equilibrium vortex lattice domains.

Magnetic order and disorder in nanomagnets probed by superconducting vortices

We have studied two nanomagnet systems with strong (Co/Pd multilayers) and weak (NdCo alloy films) stray magnetic fields by probing the out-of-plane magnetic states with superconducting vortices. The hybrid samples are made of array of nanomagnets embedded in superconducting Nb thin films. The vortex motion detects relevant magnetic state features, since superconducting vortices are able to discriminate between different magnetic stray field strengths and directions. The usual matching effect between the superconducting vortex lattice and the periodic pinning array can be quenched by means of disorder magnetic potentials with strong stray fields at random. Ordered stray fields retrieve the matching effect and yield asymmetry and shift in the vortex dissipation signal. Furthermore vortices can discriminate the sizes of the nanomagnet magnetic domains, detecting magnetic domain sizes as small as 70 nm. In addition, we observe that the vortex cores play the crucial role instead of the supercurrents around the vortex.

Orbitally limited pair-density-wave phase of multilayer superconductors

We investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic (Pauli) limiting magnetic field stabilizes a staggered layer dependent pair-density wave phase in the superconducting singlet channel. The high-field pair-density wave phase is separated from the low-field BCS phase by a first-order phase transition. The motivating guiding question in this paper is: what is the minimal necessary Maki parameter $\alpha_M$ for the appearance of the pair-density wave phase of a superconducting trilayer system? To address this problem we generalize the circular cell method for the regular flux-line lattice of a type-II superconductor to include paramagnetic depairing effects. Then, we apply the model to the trilayer system, where each of the layers are characterized by Ginzburg-Landau parameter $\kappa_0$, and a Maki parameter $\alpha_M$. We find that when the spin-orbit Rashba interaction compares to the superconducting condensation energy, the orbitally limited pair-density wave phase stabilizes for Maki parameters $\alpha_M> 10$.

Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors

It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators. This calls for new methods for engineering and manipulating of the vortex states. One of the possible routes utilizes type-1.5 superconducting layered systems with multi-scale inter-vortex interactions. In order to explore the possible vortex states that can be engineered, we present two phase diagrams of phenomenological vortex matter models with multi-scale inter-vortex interactions featuring several attractive and repulsive length scales. The phase diagrams exhibit a plethora of phases, including conventional 2D lattice phases, five stripe phases, dimer, trimer, and tetramer phases, void phases, and stable low-temperature disordered phases. The transitions between these states can be controlled by the value of an applied external field.

Effect of a dilute random field on a continuous-symmetry order parameter

XY and Heisenberg spins, subjected to strong random fields acting at few points in space with concentration $c_r \ll 1$, are studied numerically on 3d lattices containing over four million sites. Glassy behavior with strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to $c_r$ in size. The area of the hysteresis loop, $m(H)$, scales as $c_r^2$. These findings are explained by mapping the effect of strong dilute random field onto the effect of weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge density waves.

Shearing transition in a superconducting vortex lattice subject to periodic pinning

We have studied the shearing forces in a superconducting vortex system with artificial pinning sites using the Corbino geometry. Current was injected into the center of a Nb disc and propagated radially outward to produce a force in the azimuthal direction on the vortices, with strength proportional to 1/$r$. We investigated the magnetoresistance properties of the vortex lattice as a function of temperature, current, and pinning lattice configuration. The measurements show steps instead of minima at the matching field positions, indicating an unexpected influence of the pinning array on the motion of the vortex lattice. The results imply that these steps are due to a shearing transition of the vortices.

Superconducting Vortex Lattices for Ultracold Atoms

We propose and analyze a nanoengineered vortex array in a thin-film type-II superconductor as a magnetic lattice for ultracold atoms. This proposal addresses several of the key questions in the development of atomic quantum simulators. By trapping atoms close to the surface, tools of nanofabrication and structuring of lattices on the scale of few tens of nanometers become available with a corresponding benefit in energy scales and temperature requirements. This can be combined with the possibility of magnetic single site addressing and manipulation together with a favorable scaling of superconducting surface-induced decoherence.

Probing the dynamic response of antivortex, interstitial and trapped vortex lattices on magnetic periodic pinning potentials

The dynamics of the pinned vortex, antivortex and interstitial vortex have been studied in superconducting/magnetic hybrids consisting of arrays of Co/Pd multilayer nanodots embedded in Nb films. The magnetic nanodots show out-of-plane magnetization at the remanent state. This magnetic state allows for superconducting vortex lattices of different types in an applied homogeneous magnetic field. We experimentally and theoretically show three such lattices: (i) a lattice containing only antivortices; (ii) a vortex lattice entirely pinned on the dots; and (iii) a vortex lattice with pinned and interstitial vortices. Between the flux creep (low vortex velocity) and the free flux flow (high vortex velocity) regimes the interaction between the magnetic array and the vortex lattice governs the vortex dynamics, which in turn enables distinguishing experimentally the type of vortex lattice which governs the dissipation. We show that the vortex lattice with interstitial vortices has the highest onset velocity where the lattice becomes ordered, whereas the pinned vortex lattice has the smallest onset velocity. Further, for this system, we directly estimate that the external force needed to depin vortices is 60% larger than the one needed to depin antivortices; therefore we are able to decouple the antivortex–vortex motion.

Vortex lattice motion in the flux creep regime on asymmetric pinning potentials

Vortex lattice dynamics is investigated in the adiabatic regime in superconducting/magnetic nanostructures for strong and weak asymmetric pinning potentials, provided by a rectangular array of Ni triangles and a kagomé-like array of Ni dots, respectively. The AC voltage response of the AC-driven superconducting vortex lattice is measured in addition to the DC voltage response. The results allow us to link voltage rectification effects with the vortex lattice dynamics. In particular, for the weaker pinning kagomé-like array, a high-temperature zero critical current regime is identified, in which both AC and DC voltage responses can be described in terms of a simple model of thermal activation of single vortices over finite asymmetric barriers.

Superconducting Vortex Lattice Configurations on Periodic Potentials: Simulation and Experiment

Nb films have been fabricated on top of array of Ni nanodots. The array of periodic pinning potentials modifies the vortex lattice for specific values of the external applied magnetic field. By means of an implemented code developed from scratch, computer simulations based only on the vortex–vortex and the vortex–nanodot interactions provide the total interaction between vortices and pinning sites as well as the position of the vortices in the array unit cell. This simulation approach could be performed on square, rectangular or triangular arrays of nanodefects of different size.

Spin density wave induced disordering of the vortex lattice in superconducting La2−xSrxCuO4

We use small-angle neutron scattering to study the superconducting vortex lattice in La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$ as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length $\ensuremath{\xi}$ are controlled by a Van Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that spin-density-wave order acts as a source of disorder on the vortex lattice.