Current-induced self-organisation of mixed superconducting states

Wang W., Díaz-Méndez R., Wallin M., Lidmar J., Babaev E.

We study numerically the glass formation and depinning transition of a system of two-dimensional cluster-forming monodisperse particles in presence of pinning disorder. The pairwise interaction potential is nonmonotonic, and is motivated by the intervortex forces in type-$1.5$ superconductors. Such systems can form cluster glasses due to the intervortex interactions following a thermal quench, without underlying disorder. We study the effects of vortex pinning in these systems. We find that a small density of pinning centers of moderate depth has limited effect on vortex glass formation, i.e., formation of vortex glasses is dominated by intervortex interactions. At higher densities pinning can significantly affect glass formation. The cluster glass depinning, under a constant driving force, is found to be plastic, with features distinct from non-cluster-forming systems such as clusters merging and breaking. We find that in general vortices with cluster-forming interaction forces can exhibit stronger pinning effects than regular vortices.

Ooi S., Tachiki M., Konomi T., Kubo T., Kikuchi A., Arisawa S., Ito H., Umemori K.

Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

Córdoba-Camacho W.Y., Vagov A., Shanenko A.A., Aguiar J.A., Vasenko A.S., Stolyarov V.S.

Cluster formation is a focus of interdisciplinary research in both chemistry and physics. Here we discuss the exotic example of this phenomenon in the vortex matter of a thin superconductor. In superconducting films, the clustering takes place because of particular properties of the vortex interactions in the crossover or intertype regime between superconductivity types I and II. These interactions are controlled by the two parameters that are responsible for the crossover, Ginzburg-Landau parameter κ, which specifies the superconducting material of the film, and film thickness d, which controls effects due to stray magnetic fields outside the sample. We demonstrate that their competition gives rise to a complex spatial dependence of the interaction potential between vortices, favoring the formation of chainlike vortex clusters.

Biswas P.K., Rybakov F.N., Singh R.P., Mukherjee S., Parzyk N., Balakrishnan G., Lees M.R., Dewhurst C.D., Babaev E., Hillier A.D., Paul D.M.

Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example at different temperatures is rare in nature. We the employed muon spin rotation (muSR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most importantly, we found a region showing unusual behavior where the usually mutually exclusive muSR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modeling that required taking into account multiple bands and multiple coherence lengths, which suggests that material has one coherence length larger and another smaller than the magnetic field penetration length (the type-1.5 regime). At stronger fields, a footprint of the type-II mixed state showing square flux-line lattice was also obtained using neutron diffraction.

Kogan V.G., Prozorov R.

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 $vv_c(T)$, 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.

Dobrovolskiy O.V., Vodolazov D.Y., Porrati F., Sachser R., Bevz V.M., Mikhailov M.Y., Chumak A.V., Huth M.

The ultra-fast dynamics of superconducting vortices harbors rich physics generic to nonequilibrium collective systems. The phenomenon of flux-flow instability (FFI), however, prevents its exploration and sets practical limits for the use of vortices in various applications. To suppress the FFI, a superconductor should exhibit a rarely achieved combination of properties: weak volume pinning, close-to-depairing critical current, and fast heat removal from heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion at velocities of 10–15 km s−1 in a directly written Nb-C superconductor with a close-to-perfect edge barrier. The spatial evolution of the FFI is described using the edge-controlled FFI model, implying a chain of FFI nucleation points along the sample edge and their development into self-organized Josephson-like junctions (vortex rivers). In addition, our results offer insights into the applicability of widely used FFI models and suggest Nb-C to be a good candidate material for fast single-photon detectors. To realize ultra-fast dynamics of superconducting vortices one needs to overcome the practical issue of flux-flow instability (FFI). Here, Dobrovolskiy et al. demonstrate ultra-fast vortex motion at 10-15 km/s velocity in a Nb-C superconductor where the FFI is described by the edge-controlled FFI model.

Vagov A., Wolf S., Croitoru M.D., Shanenko A.A.

Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic flux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such configurations has not been presented. We solve this old-standing fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic configurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the self-duality of the theory that is universal and not sensitive to the microscopic details. Classification into type I and II reflects different responses of a superconductor to an applied magnetic field, however, there are intertype materials with unique properties and atypical vortex configurations. The authors study vortex patterns in this regime revealing that their properties are governed by a universal material independent mechanism, which amends the dual classification.

Backs A., Schulz M., Pipich V., Kleinhans M., Böni P., Mühlbauer S.

In the intermediate mixed state (IMS) of type-II/1 superconductors, vortex lattice (VL) and Meissner state domains coexist due to a partially attractive vortex interaction. Using a neutron-based multiscale approach combined with magnetization measurements, we study the continuous decomposition of a homogeneous VL into increasingly dense domains in the IMS in bulk niobium samples of varying purity. We find a universal temperature dependence of the vortex spacing, closely related to the London penetration depth and independent of the external magnetic field. The rearrangement of vortices occurs even in the presence of a flux freezing transition, i.e. pronounced pinning, indicating a breakdown of pinning at the onset of the vortex attraction.

Wolf S., Vagov A., Shanenko A.A., Axt V.M., Aguiar J.A.

This work investigates interactions of vortices in superconducting materials between standard types I and II, in the domain of the so-called intertype (IT) superconductivity. Contrary to common expectations, the many-body (many-vortex) contribution is not a correction to the pair-vortex interaction here but plays a crucial role in the formation of the IT vortex matter. In particular, the many-body interactions stabilize vortex clusters that otherwise could not exist. Furthermore, clusters with large numbers of vortices become more stable when approaching the boundary between the intertype domain and type I. This indicates that IT superconductors develop a peculiar unconventional type of the vortex matter governed by the many-body interactions of vortices.

Reimann T., Schulz M., Mildner D.F., Bleuel M., Brûlet A., Harti R.P., Benka G., Bauer A., Böni P., Mühlbauer S.

Vortex attraction which can cause a bundling of vortices has been observed in a multitude of type-II superconductors. While its underlying mechanisms have been extensively studied, the morphology of the emerging vortex superstructure has only been rarely considered. Here, we present a comprehensive experimental study on the type-II/1 superconductor niobium which focuses on the transformation of its homogeneous vortex lattice into an inhomogeneous domain structure at the onset of vortex attraction. By means of small-angle neutron scattering, ultra-small-angle neutron scattering, and neutron grating interferometry, the vortex lattice and the micrometer-scale vortex domain structure as well as its distribution could be investigated. In particular, we focus on the transformation of the vortex lattice at the transition to the intermediate mixed state, which is characterized by vortex attraction. We have found that the phase separation of the vortex lattice into an irregular domain structure takes place via a process showing strong similarity to spinodal decomposition. While pinning disorders the domain morphology, the characteristic length scale of the domain structure is governed by an interplay of field distortion energy and domain surface tension. Finally, geometric barriers in the disk-shaped samples provoke an inhomogeneous distribution of domains on the macroscopic scale.

Babaev E., Carlström J., Silaev M., Speight J.M.

Embon L., Anahory Y., Jelić Ž.L., Lachman E.O., Myasoedov Y., Huber M.E., Mikitik G.P., Silhanek A.V., Milošević M.V., Gurevich A., Zeldov E.

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here, we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities of up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications.Ultrafast vortex dynamics driven by strong currents define eletromagnetic properties of superconductors, but it remains unexplored. Here, Embon et al. use a unique scanning microscopy technique to image steady-state penetration of super-fast vortices into a superconducting Pb film at rates of tens of GHz and velocities up to tens of km/s.

Vagov A., Shanenko A.A., Milošević M.V., Axt V.M., Vinokur V.M., Aguiar J.A., Peeters F.M.

In the nearest vicinity of the critical temperature, types I and II of conventional single-band superconductors interchange at the Ginzburg-Landau parameter $\ensuremath{\kappa}=1/\sqrt{2}$. At lower temperatures this point unfolds into a narrow but finite interval of $\ensuremath{\kappa}$'s, shaping an intertype (transitional) domain in the $(\ensuremath{\kappa},T)$ plane. In the present work, based on the extended Ginzburg-Landau formalism, we show that the same picture of the two standard types with the transitional domain in between applies also to multiband superconductors. However, the intertype domain notably widens in the presence of multiple bands and can become extremely large when the system has a significant disparity between the band parameters. It is concluded that many multiband superconductors, such as recently discovered borides and iron-based materials, can belong to the intertype regime.

Dewhurst C.D., Grillo I., Honecker D., Bonnaud M., Jacques M., Amrouni C., Perillo-Marcone A., Manzin G., Cubitt R.

The D33 small-angle neutron scattering (SANS) instrument at the Institut Laue–Langevin (ILL) is the most recent SANS instrument to be built at the ILL. In a project beginning in 2005 and lasting seven years, the concept has been developed, and the instrument designed, manufactured and installed. D33 was commissioned with neutrons during the second half of 2012, fully entering the ILL user programme in 2013. The scientific case required that D33 should provide a wide dynamic range of measured scattering vector magnitudeq, flexibility with regard to the instrument resolution, and the provision of polarized neutrons and3He spin analysis to facilitate and expand studies in magnetism. In monochromatic mode, a velocity selector and a flexible system of inter-collimation apertures define the neutron beam. A double-chopper system enables a time-of-flight (TOF) mode of operation, allowing an enhanced dynamicqrange (qmax/qmin) and a flexible wavelength resolution. Two large multitube detectors extend the dynamicqrange further, givingqmax/qmin≃ 25 in monochromatic mode and a very largeqmax/qmin> 1000 in TOF mode. The sample zone is large and flexible in configuration, accommodating complex and bulky sample environments, while the position of D33 is such as to allow high magnetic fields at the sample position. The instrument is of general purpose with a performance rivalling that of D22, and is well adapted for SANS studies in scientific disciplines as diverse as solution scattering in biology and soft matter and studies of physics, materials science and magnetism. This article provides a detailed technical description of D33 and its performance and characterization of the individual components, and serves as a technical reference for users of the instrument.

Reimann T., Mühlbauer S., Schulz M., Betz B., Kaestner A., Pipich V., Böni P., Grünzweig C.

Alike materials in the solid state, the phase diagram of type-II superconductors exhibit crystalline, amorphous, liquid and spatially inhomogeneous phases. The multitude of different phases of vortex matter has thence proven to act as almost ideal model system for the study of both the underlying properties of superconductivity but also of general phenomena such as domain nucleation and morphology. Here we show how neutron grating interferometry yields detailed information on the vortex lattice and its domain structure in the intermediate mixed state of a type-II niobium superconductor. In particular, we identify the nucleation regions, how the intermediate mixed state expands, and where it finally evolves into the Shubnikov phase. Moreover, we complement the results obtained from neutron grating interferometry by small-angle neutron scattering that confirm the spatially resolved morphology found in the intermediate mixed state, and very small-angle neutron scattering that confirm the domain structure of the vortex lattice. The phase diagram of type-II superconductors exhibits a multitude of different phases, whose study can shed light on domain nucleation and morphology. Here the authors use neutron grating interferometry to investigate the nucleation and phase changes of an intermediate mixed state in a niobium superconductor.

Brems X.S., Muehlbauer S., Cubitt R.

Abstract The intermediate mixed state under the influence of a transport current was studied using small angle neutron scattering. The internal magnetic domain structure consisting of mixed state domains and flux free Meissner state domains was observed to rearrange at intermediate currents well before the critical depinning current marked by a finite voltage. The local rearrangement can be traced by the changes in the vortex lattice Bragg peak scattering and the current-induced anisotropy of the low-q scattering connected to the internal magnetic domain structure. It is argued, that the local reorganisation prior to the critical depinning current is inherently linked to the interplay of the pinning landscape with the vortex lattice domain structure governed by the physics of the intermediate mixed state.

Brems X.S., Mühlbauer S., Cubitt R.

Small-angle neutron scattering is a widely used technique to study large-scale structures in bulk samples. The largest accessible length scale in conventional Bragg scattering is determined by the combination of the longest available neutron wavelength and smallest resolvable scattering angle. A method is presented that circumvents this limitation and is able to extract larger length scales from the low-q power-law scattering using a modification of the well known Porod law connecting the scattered intensity of randomly distributed objects to their specific surface area. It is shown that in the special case of a highly aligned domain structure the specific surface area extracted from the modified Porod law can be used to determine specific length scales of the domain structure. The analysis method is applied to study the micrometre-sized domain structure found in the intermediate mixed state of the superconductor niobium. The analysis approach allows the range of accessible length scales to be extended from 1 µm to up to 40 µm using a conventional small-angle neutron scattering setup.

Neverov V.D., Lukyanov A.E., Krasavin A.V., Shanenko A.A., Croitoru M.D., Vagov A.

Reichhardt C., Reichhardt C.J.

de Araujo Sarmento M., Cordoba W.Y., Shanenko A., Vagov A., Aguiar J.A., Stolyarov V.S.

Abstract To describe the way complexity emerges in seemingly simple systems of nature, requires one to attend to two principal questions: how complex patterns appear spontaneously and why a single system can accommodate their inexhaustible variety. It is commonly assumed the pattern formation phenomenon is related to the competition of several types of interactions with disparate length scales. These multi-scale interactions also lead to frustration within the system, resulting in the existence of a manifold of configurations-patterns with qualitatively distinct morphologies. This work explores an alternative approach through a mechanism that leads to a wide range of intricate and topologically non-trivial patterns. The mechanism is described by the self-dual Ginzburg-Landau theory and, possibly, other Maxwell–Higgs models. It gives rise to unique spatial flux and condensate spatial profiles observed in superconductors between the two conventional superconductivity types I and II.

Marychev P.M., Shanenko A.A., Vagov A.V.

Nonmagnetic impurity scattering is known to shift up the Ginzburg–Landau parameter κ of a superconductor. In this case, when the system is initially in type I, it can change its magnetic response, crossing the intertype domain with κ ∼ 1 between the two standard superconductivity types and arriving at type II. In the present work we demonstrate that the impact of disorder can be much more profound in the presence of the multiband structure of the charge carrier states. In particular, when the band diffusivities differ from each other, the intertype domain tends to expand significantly, including points with κ ≫ 1 that belong to deep type-II in conventional single-band superconductors. Our finding sheds light on the nontrivial disorder effect and significantly complements earlier results on the enlargement of the intertype domain in clean multiband superconductors.

Marychev P.M., Chen Y.

Vagov A., Saraiva T.T., Shanenko A.A., Vasenko A.S., Aguiar J.A., Stolyarov V.S., Roditchev D.

AbstractIn many pnictides the superconductivity coexists with ferromagnetism in an accessible range of temperatures and compositions. Recent experiments revealed that when the temperature of magnetic ordering Tm is below the superconducting transition temperature Tc, highly non-trivial physical phenomena occur. In this work we demonstrate the existence of a temperature window, situated between Tm and Tc, where these intrinsically type-II superconductors are in the intertype regime. We explore analytically and numerically its rich phase diagram characterized by exotic spatial flux configurations—vortex clusters, chains, giant vortices and vortex liquid droplets—which are absent in both type-I and type-II bulk superconductors. We find that the intertype regime is almost independent of microscopic parameters, and can be achieved by simply varying the temperature. This opens the route for experimental studies of the intertype superconductivity scarcely investigated to date.

Backs A., Al-Falou A., Vagov A., Böni P., Mühlbauer S.

In the vicinity of the type-I/type-II crossover in conventional superconductors, vortices exhibit a nonmonotonic interaction, which leads to exotic vortex matter states. We perform molecular dynamics simulations on a model superconductor in the intertype regime. In a field cooled approach, we examine the transition of a homogeneous vortex lattice (VL) into a structure consisting of VL domains and Meissner-state domains. The results show extraordinary stability of the transition against vortex pinning and a strong dependence on the external magnetic field.

Vagov A., Nikonov E.G.