Dynamical visualization of attractively interacting single vortices in type-II/1 superconducting Nb by magneto-optical imaging

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.

Prozorov R., Zarea M., Sauls J.A.

Niobium is one of the most researched superconductors, both theoretically and experimentally. It is enormously significant in all branches of superconducting applications, from powerful magnets to quantum computing. It is therefore imperative to understand its fundamental properties in great detail. Here, we use the results of recent microscopic calculations of anisotropic electronic, phonon, and superconducting properties, and apply a thermodynamic criterion for the type of superconductivity, more accurate and straightforward than a conventional Ginzburg-Landau parameter $\ensuremath{\kappa}$-based delineation, to show that pure niobium is a type-I superconductor in the clean limit. However, disorder (impurities, defects, strain, stress) pushes it to become a type-II superconductor.

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.

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.

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.

Veshchunov I.S., Magrini W., Mironov S.V., Godin A.G., Trebbia J.-., Buzdin A.I., Tamarat P., Lounis B.

Magnetic field can penetrate into type II superconductors in the form of Abrikosov vortices, which are magnetic flux tubes surrounded by circulating supercurrents often trapped at defects referred to as pinning sites. Although the average properties of the vortex matter in superconductors can be tuned with magnetic fields, temperature or electric currents, handling of individual Abrikosov vortices remains challenging and has been demonstrated only with sophisticated scanning local probe microscopies. Here we introduce a far-field optical method based on local heating of the superconductor with a focused laser beam to realize a fast and precise manipulation of individual vortices, in the same way as with optical tweezers. This simple approach provides the perfect basis for sculpting the magnetic flux profile in superconducting devices like a vortex lens or a vortex cleaner, without resorting to static pinning or ratchet effects.

Huang S., Kubo T., Geng R. .

Recent studies by Romanenko et al. revealed that cooling down a superconducting cavity under a large spatial temperature gradient decreases the amount of trapped flux and leads to reduction of the residual surface resistance. In the present paper, the flux expulsion ratio and the trapped-flux-induced surface resistance of a large-grain cavity cooled down under a spatial temperature gradient up to $80\text{ }\text{ }\mathrm{K}/\mathrm{m}$ are studied under various applied magnetic fields from 5 to $20\text{ }\text{ }\ensuremath{\mu}\mathrm{T}$. We show the flux expulsion ratio improves as the spatial temperature gradient increases, independent of the applied magnetic field: our results support and enforce the previous studies. We then analyze all rf measurement results obtained under different applied magnetic fields together by plotting the trapped-flux-induced surface resistance normalized by the applied magnetic field as a function of the spatial temperature gradient. All the data can be fitted by a single curve, which defines an empirical formula for the trapped-flux-induced surface resistance as a function of the spatial temperature gradient and applied magnetic field. The formula can fit not only the present results but also those obtained by Romanenko et al. previously. The sensitivity ${r}_{\mathrm{fl}}$ of surface resistance from trapped magnetic flux of fine-grain and large-grain niobium cavities and the origin of $dT/ds$ dependence of ${R}_{\mathrm{fl}}/{B}_{a}$ are also discussed.

Posen S., Checchin M., Crawford A.C., Grassellino A., Martinello M., Melnychuk O.S., Romanenko A., Sergatskov D.A., Trenikhina Y.

Even when cooled through its transition temperature in the presence of an external magnetic field, a superconductor can expel nearly all external magnetic flux. This paper presents an experimental study to identify the parameters that most strongly influence flux trapping in high purity niobium during cooldown. This is critical to the operation of superconducting radiofrequency cavities, in which trapped flux degrades the quality factor and therefore cryogenic efficiency. Flux expulsion was measured on a large survey of 1.3 GHz cavities prepared in various ways. It is shown that both spatial thermal gradient and high temperature treatment are critical to expelling external magnetic fields, while surface treatment has minimal effect. For the first time, it is shown that a cavity can be converted from poor expulsion behavior to strong expulsion behavior after furnace treatment, resulting in a substantial improvement in quality factor. Microscopic investigations are performed to study the relevant changes in the material from this treatment. Future plans are described to build on this result in order to optimize treatment for future cavities.

Kimura N., Kabeya N., Saitoh K., Satoh K., Ogi H., Ohsaki K., Aoki H.

We report the specific heat and ac magnetic susceptibility of noncentrosymmetric superconductor LaRhSi3. A first-order superconducting transition is observed in specific heat C under different magnetic field values. The C(T) values in zero-field-cooling and field-cooling processes become different at a magnetic field between 20 and 130 Oe. These results suggest that conversion from type-I to type-II/1 superconductivity is realized in LaRhSi3. The ac susceptibility indicates that surface superconductivity with an extremely high limiting field occurs probably due to the conversion temperature.

Tachiki M., Koizumi H.

The electron pairing in the topological superconductor has been predicted to be spin-triplet pairing with odd parity. If the superconducting carries have a magnetic moment, the magnetization arising from it reduces the repulsive interaction between the vortices, thus the vortex density drastically increases in the region above the lower critical magnetic field ${H}_{c1}$. The comparison of the theoretical calculation with the experimental result by Das et al. [Phys. Rev. B 83, 220513(R) (2011)] indicates that the magnetization is small, suggesting that it is not a spin-triplet superconductor. The theory suggests that if the nonzero magnetization arises from the supercurrent carriers a hysteresis in the magnetization curve around ${H}_{c1}$ may be observed. The observation (or nonobservation) of it will narrow down the mechanism of the superconductivity in ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$.

Gurevich A., Ciovati G.

We present detailed experimental and theoretical investigations of hotspots produced by trapped vortex bundles and their effect on the radio-frequency (rf) surface resistance ${R}_{s}$ of superconductors at low temperatures. Our measurements of ${R}_{s}$, combined with the temperature mapping and laser scanning of a 2.36-mm-thick Nb plate incorporated into a 3.3-GHz Nb resonator cavity cooled by the superfluid He at 2 K, revealed spatial scales and temperature distributions of hotspots and showed that they can be moved or split by thermal gradients produced by the scanning laser beam. These results, along with the observed hysteretic field dependence of ${R}_{s}$ which can be tuned by the scanning laser beam, show that the hotspots in our Nb sample are due to trapped vortex bundles which contain $\ensuremath{\sim}{10}^{6}$ vortices spread over regions $\ensuremath{\sim}0.1--1$ cm. We calculated the frequency dependence of the rf power dissipated by oscillating vortex segments trapped between nanoscale pinning centers, taking into account all bending modes and the nonlocal line tension of the vortex driven by rf Meissner currents. We also calculated the temperature distributions caused by trapped vortex hotspots, and suggested a method of reconstructing the spatial distribution of vortex dissipation sources from the observed temperature maps. Vortex hotspots can dominate the residual surface resistance at low temperatures and give rise to a significant dependence of ${R}_{s}$ on the rf field amplitude ${H}_{p}$, which can have important implications for the rf resonating cavities used in particle accelerators and for thin-film structures used in quantum computing and photon detectors.

Koyama T., Machida M.

The conventional Ginzburg–Landau (GL) theory is extended to a nonlocal one. In this nonlocal GL theory the superconducting current becomes nonlocal. The magnetic field distribution calculated in the single vortex state indicates that the interaction between vortices has an attractive part in low- κ type II superconductors with κ κ c  ∼ 1. The attractive interaction causes the first-order transition at H c 1 .

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

A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth \lambda and the coherence length \xi. Their ratio \kappa determines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when \kappa 1/\sqrt{2} . We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate "type-1.5" superconducting state when, e.g. in two-component case \xi_1

Schindelin J., Arganda-Carreras I., Frise E., Kaynig V., Longair M., Pietzsch T., Preibisch S., Rueden C., Saalfeld S., Schmid B., Tinevez J., White D.J., Hartenstein V., Eliceiri K., Tomancak P., et. al.

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