Superconducting proximity effect currents in Indium above its transition

In this paper, complex Ginzburg-Landau (CGL) equations governed by p-Laplacian are studied. We discuss the global existence of solutions for the initial-boundary value problem of the equation in general domains. The global solvability of the initialboundary value problem for the case when p = 2 is already examined by several authors provided that parameters appearing in CGL equations satisfy a suitable condition. Our approach to CGL equations is based on the theory of parabolic equations with nonmonotone perturbations. By using this method together with some approximate procedure and a diagonal argument, the global solvability is shown without assuming any growth conditions on the nonlinear terms.

While the global demand for energy continues to grow, the world’s depots of fossil fuels decrease. Logically, scientists have researched in different ways of creating sustainable energy. Dams, solar power and wind energy are all different ways of extracting power from nature. Having neither mountains nor many hours of annual sunshine, Denmark is, however, a flat country with many kilometers of coast line and calm weather, and therefore is perfectly suited for wind energy. Because of these facts, Denmark has always been a pioneer within the wind industry, building the world’s first off-shore wind energy park in 1991. In recent years, wind turbines have grown dramatically in size and capacity. Scientists predict that in order to make wind energy a more suitable alternative to fossil fuels, the wind turbines have to become even larger. The major problem with these super wind turbines, however, is the weight of the nacelle, of which a heavy part is the gear box. In order to avoid having a gear box in the wind turbine, a direct driven generator has been proposed, where superconductors play an important role. Energy losses due to Joule heating will be eliminated and high temperature superconductors are capable of working in high magnetic fields (several Teslas). The alternative to superconductors are permanent magnets, but the required amount would become expensive and inaccessible, while superconductors can be made from easily accessible elements. However, using superconductors also pose considerable challenges; low temperature cooling systems are required and the superconductors need to be of high quality. High temperature superconductors is a relatively new field of study, with the first discoveries made in the 1980s. Having found materials with superconducting properties at relatively high temperatures, the issue of optimizing other properties arose. A pinning center is an irregularity in the crystal, which destroys the superconducting properties. Here the magnetic field lines can penetrate without causing further damage to the superconductor. In 2005 Misko et al. found that a gradient in density of pinning centers could increase the critical current density (Jc) in a magnetic field. Pinning centers had been known to optimize superconductors, but with this new information, scientists have been equipped with a new tool to make superconductors more suitable for wind turbines. Since Misko et al. first predicted that different pinning densities throughout the superconductor could improve superconductors; many attempts have been made in order to show this property experimentally. Different methods to create the desired pinning patterns experimentally include Molecular Beam Epitaxy and E-beam Lithography. These methods are, however, both very expensive, making them less attractive for industrial production. This project investigates different options of creating simple gradients in the pinning center density.

<p indent="0mm">The discovery of F-doped LaFeAsO in 2008 brought a worldwide research surge of iron-based superconductors. As a new type of high-temperature superconductors, iron-based superconductors have attracted much attention due to their unique properties and significant differences from copper oxide and traditional superconductors. Iron-based superconductors have small anisotropy, high superconducting transition temperature and upper critical field, which are preferred in film preparation and applications. At the same time, the features of iron-based superconductor films, such as higher superconducting transition temperature in epitaxial films and the ability to stabilize metastable equivalents, are interesting to the researchers. The studies on films are very useful for the basic research on superconducting physics and the search of new superconducting materials. The iron-based superconductors discovered so far can be divided into four systems: (1) 1111 system: LnFeAs (O, F) (Ln= lanthanides); (2) 122 system: AEFe₂As₂ (AE = alkaline earth metals); (3) 111 system: LiFeAs and NaFeAs; (4) 11 system: FeCh (Ch=chalcogenides). 1111 system is the first reported iron-based superconductor. It has a high critical transition temperature up to <sc>58 K</sc> as well as a higher upper critical field. The disadvantage of 1111 superconductors is the lager anisotropy and the broadened superconducting transition under the magnetic field. The critical transition temperature of 122 system is lower than 1111 system, but it can still reach <sc>38 K,</sc> and its anisotropy and elemental stability is better than 1111 system. The structure of 11 system is the simplest in iron-based superconductor family. It contains no toxic element As, but the transition temperature is low <sc>(8 K).</sc> 111 system is unstable in the air, limiting its application prospects. In addition, the critical current density is very important for the application of superconductors, which has been obtained in 122-system superconducting tapes. Meanwhile, the 11-system superconducting film stands out because of its easy growth, simple structure and high transport current density, which can exceed <sc>10⁵ A/cm²</sc> even at <sc>30 T.</sc> During the past years, researchers around the world have made great progress in the fabrication and synthesis of iron-based superconducting single crystals, bulk materials, tapes and thin films. Among them, the development of thin films cannot be ignored. The fabrication of high-quality thin films has three purposes: Basic research, tape application and electronic application. Basic and application-oriented research is developing quickly. Increasing the critical current density is an important strategy for realizing commercialized and cost-effective high-temperature superconductor technology, which can be improved by microstructure engineering. Naturally grown pinning centers and artificial pinning centers are able to pin on magnetic vortices in magnetic fields, which can effectively prevent the dissipation of energy and raise critical current density. Based on the results achieved in 1111 system, doped 122 system, and 11 system, we analyzed the possible connections between the growth technique, microstructure and superconducting properties of iron-based superconducting films.

The effects of spin-polarized quasiparticle transport in superconducting YBa2Cu3O7-delta (YBCO) epitaxial films are investigated by means of current injection into perovskite ferromagnet-insulator-superconductor (F-I-S) heterostructures. These effects are compared with the injection of simple quasiparticles into control samples of perovskite nonmagnetic metal-insulator-superconductor (N-I-S). Systematic studies of the critical current density (J(c)) as a function of the injection current density (J(inj)), temperature (T), and the thickness (d) of the superconductor reveal drastic differences between the F-I-S and N-I-S heterostructures, with strong suppression of J(c) and a rapidly increasing characteristic transport length near the superconducting transition temperature T-c only in the F-I-S samples. The temperature dependence of the efficiency (etaequivalent toDeltaJ(c)/J(inj); DeltaJ(c): the suppression of critical current due to finite J(inj)) in the F-I-S samples is also in sharp contrast to that in the N-I-S samples, suggesting significant redistribution of quasiparticles in F-I-S due to the longer lifetime of spin-polarized quasiparticles. Application of conventional theory for nonequilibrium superconductivity to these data further reveal that a substantial chemical potential shift mu(*) in F-I-S samples must be invoked to account for the experimental observation, whereas no discernible chemical potential shift exists in the N-I-S samples, suggesting strong effects of spin-polarized quasiparticles on cuprate superconductivity. The characteristic times estimated from our studies are suggestive of anisotropic spin relaxation processes, possibly with spin-orbit interaction dominating the c-axis spin transport and exchange interaction prevailing within the CuO2 planes. Several alternative scenarios attempted to account for the suppression of critical currents in F-I-S samples are also critically examined, and are found to be neither compatible with experimental data nor with the established theory of nonequilibrium superconductivity.

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2. If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation. The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text. The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices. We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

This thesis presents the use of superconductivity as a structural probe for studying amorphous and metastable materials. The characteristics of the superconducting state which facilitate its use as a probe are explained, followed by a description of some of the properties of the materials studied. The superconducting measurements performed were critical current, transition temperature and upper critical field. Materials prepared by rapid quench from the melt, sputter deposition and ion beam mixing were studied. The critical current measurements performed on liquid quenched materials reflect three pinning mechanisms. Crystalline inclusions in otherwise amorphous (Mo0.6Ru0.4)80Si10B10 produced a dramatic increase in critical current. The pinning in purely amorphous (Mo0.6Ru0.4)82B18 was shown to be affected by pinning by surface roughness on the sample edges. This contribution can be eliminated by a proper sample geometry and electropolish treatment. The bulk pinning in purely amorphous (Mo0.6Ru0.4)82B18 was shown to first decrease and then increase as a function of annealing time. This reflects the disappearance of quenched in inhomogeneous strains and excess volume defects followed by the growth of an inhomogeneity such as compositional phase segregation during an anneal. The upper critical field was measured for liquid quenched (Mo0.6Ru0.4)1-xBx for x = 0.12, 0.18 and 0.22 both before and after an anneal. The annealed samples exhibited greater transition widths and more curvature in the Hc2(T) curves than the unannealed samples which are evidence for a growth of inhomogeneities upon annealing. Measurements on sputter deposited (Mo0.6Ru0.4)82B18 were performed on samples sputtered in low (5 µm) and high (75 µm) Ar pressure, The material sputtered in low Ar pressure had a greater drop in Tc than the liquid quenched material and a pinning profile which exhibited a peak near Hc2. The sample sputtered in high Ar pressure was very inhomogeneous as evidenced by transition width and flux pinning force profile. Measurements were performed on ion beam mixed Mo55Ru45. The structure consisted of an amorphous matrix with crystalline inclusions. The pinning profile was characteristic of a strong pinning mechanism. The pinning force decreased then increased as a function of ion beam dose. This reflects the destruction of the remnants of the original structure followed by the formation of an inhomogeneity such as σ-MoRu or Xe gas bubbles during ion beam irradiation.

In a previous study (2017 Phys. Rev. B 96 144501), a strong variation in the superconducting transition temperature T c of YB6 differing by a factor of two has been explained by a change in the density of yttrium and boron vacancies tuning the electron–phonon interaction. Here, by using an array of miniature Hall probes, we address the penetration of the magnetic field, pinning, and critical current density on a series of YB6 single crystals with T c variation between 4.25 and 7.35 K. The analysis of the superconducting and normal-state specific heat characteristics allowed us to determine T c and the stoichiometry of our samples. We observed almost no pinning in the most stoichiometric YB6 crystal with the lowest T c. Upon increasing the number of vacancies weak pinning appears, and the critical current density is enhanced following the increased transition temperature in a linear variation. We argue that such an increase is, within weak collective pinning theory, consistent with the increasing number of vacancies that serve as pinning centers.

Two types of growth processes of Y-Ba-Cu-O thin films were investigated: three step processes involving post deposition high temperature anneals, and in situ growth processes. Films were deposited by sequential ion beam sputtering from elemental Y, Ba and Cu targets, and characterized by x-ray diffraction, transmission and scanning electron microscopy, energy dispersive x-ray analysis, Rutherford backscattering spectrometry, and low temperature resistivity measurements. In the three step process, multilayers of ~60 A periodicity were deposited on (001) SrTiO3, annealed in oxygen at 850-900°C, and subsequently at 400-500°C, to obtain the superconducting YBa2Cu3O7-δ phase. The films were epitaxial, predominantly single phase YBa2Cu3O7-δ, with different orientations. The nucleation and growth of Y-Ba-Cu-O films deposited on (001) SrTiO3 by magnetron sputtering from separate Y, BaF2 and Cu sources and grown by a three step process, was investigated by transmission electron microscopy. The in situ growth of YBa2Cu3O7-δ films by sequential ion beam sputtering was investigated. The films were deposited following the stacking sequence of YBa2Cu3O7-δ, with the individual layer thicknesses nominally equal to one monolayer, at temperatures between 550 and 750°C. O2 was supplied during growth. Epitaxial, c-axis oriented YBa2Cu3O7-δ films were obtained on MgO and SrTiO3. The correlations between deposition parameters, and structural and electrical properties were investigated. The films had expanded c-axis lattice parameters. The superconducting transition temperatures decreased with the enlargement of the c-lattice parameter. The deposition temperature was the main parameter controlling the lattice expansion. This was later interpreted in terms of the thermally activated dissociation of O2 at the film surface. We proposed that the expansion of the c-lattice parameter was a consequence of kinetic limitations to the incorporation of oxygen into the films during growth. This led to a consistent description of the results obtained in this work, and results reported in the literature for other in situ growth techniques. The films also presented inhomogeneous lattice distortions along the c-direction, that were larger for films with large lattice parameters. The superconducting transitions were broader for films with large inhomogeneous strains. The microstructure of films grown on several substrates (SrTiO3, MgO, SiO2/Si) under different growth conditions was investigated.

Experimental investigations were made on the transport properties of several superconducting systems in which the superconducting state was out of thermodynamic equilibrium. In such systems, the dynamics of the pairing processes governs the restoration of equilibrium. Systematic investigations into the nonequilibrium dynamics were made possible by creating a steady state depairing region at a supernormal interface with a transport current. Information Was obtained by direct probing of the potential profiles in the depairing region. Measurements were made with superconducting microcircuits with high spatial resolution extending to the scale of the wavelength of light which limits our fabrication system. It was found that at the depairing region, the experimental results can be described by the existence of two distinct potentials, one for the single electron excitations and one for the electron pairs. A theory for the dynamics of the nonequilibrium process was proposed and succeeded in accounting for most of the experimental observations. The relaxation time associated with this dynamics is found to be longer than the usual equilibrium relaxation time for the condensed electron pairs. Similar measurements were extended to nonequilibrium regions close to current carrying interfaces between two different superconductors. In this case it was found that the two-potential measurements performed within the nonequilibrium region can be described in terms of a time dependent boundary condition at the interface. To study the nonequilibrium superconductivity associated with this time dependent boundary condition in a controlled way, two such superconducting boundaries were brought very close to each other, creating a well defined boundary region less than one micron in length. It was found that the boundary region showed Josephson-like effects as well as a unique phenomenon in which electromagnetic radiation increases the apparent superconducting transition temperature. A model for this situation was proposed in which two complex wavefunctions with independent phase angles interfere quantum mechanically inside the boundary region. This model successfully explains most of the observed phenomena associated with the boundary region in the voltage sustaining nonequilibrium state.

The heterogeneous properties around the interface between ferromagnet (F) and conventional s-wave superconductor (S) hybrid structures exhibit several remarkable phenomena. The superconductivity and ferromagnetism are two competing orders. The ferromagnetic order forces the spins to align in parallel, and Cooper pairs in singlet superconductivity prefer an antiparallel spin orientation with total spin zero. Due to the incompatible nature of S and F, singlet superconductivity and ferromagnetic order should not coexist in bulk materials. Thus, fabricating S/F heterostructure is the immediate way to study the proximity phenomena in the competition of the two order parameters. However, the S/F proximity effect has attracted much attention over the past years. Aspect of the S/F proximity effect, the “inverse proximity” effect which is the ferromagnetic order-parameter penetrates into the superconductor, has gained renewed interest only in the last decade. Following the literatures, the characterizations of the S/F lateral junction have been studied rear, especially the inverse proximity. Therefore, it gives us the motivations to study the inverse proximity effect in S/F lateral junction. In this dissertation, we systematically investigate the lateral S/F junctions by electron transport measurement. We fabricated two types of S/F lateral junction. One is the junctions between two superconductor Nb leads were connected by two bars of the ferromagnetic NiFe, another is lateral Josephson junction with a weak link by fabricating a ferromagnetic NiFe strip across a superconducting Nb strip. In the lateral two NiFe bars junctions, the separation distance l between NiFe bars was varied from 150 to 700 nm to study the spin relaxation effect in Nb. In small l (150 and 250 nm) samples, a spin-valve like behavior related to the inverse proximity effect was observed, which manifest itself as charge accumulation due to spin imbalance near the interface. However, for samples with large l (500 and 700 nm), the spin-valve behavior vanishes and the anisotropic magnetoresistance effect dominates. The spin-valve and anisotropic magnetoresistance (AMR) behaviors were also observed on multiple bars samples. From the two different behaviors observation, the spin relaxation length of Nb lateral device can be estimated. The transition temperature enhancement of Nb was observed on the spin-valve behavior samples. The transition temperature enhancement of the l = 250 and 300 nm samples are 35.5 and 58.3 mK, respectively. In addition, there are some striking resistance peaks observed in the R-T measurements. It is attributed to the interaction between S and F. In the lateral Josephson junctions with a weak link by fabricating a ferromagnetic NiFe strip across superconducting Nb strips. We argue that the effective weak link of the Josephson junction was induced by the inverse proximity effect around the Nb interface in contact with the NiFe. The argument has been proved by the observation of the dc and ac Josephson effect. We also estimated the strength of the Josephson junctions by Thouless energy analysis. In our observations, the supercurrents can go through such long distance up to 2.1μm of the junctions, implying that a spin triplet component possibly exists as the theoretical prediction, the spin triplet component induced by inverse proximity effect. In addition, we also discussed the correlation of the vortex dynamics and the critical current modulations, and ruled out the possibility of the vortex dynamics in our data.

Homogeneity of superconducting properties in SmBa 2Cu 3O 7 − δ-seeded melt processed YBCO

Properties of strong-coupled MgB2 nanobridges fabricated by focused ion beam

This work concentrates on the study of high-temperature superconducting thin epitaxial films composed of YBCO. Further, in the second part a ferromagnetic layer of LCMO is added to the superconductor. All the films were investigated with a magneto-optical technique capable of directly imaging the critical current distribution in the sample. Mainly temperature dependent measurements were performed. By applying a systematical quantitative analysis of the temperature dependent critical current, different flux-pinning mechanisms could be identified to limit the critical current in different temperature regimes. Comparison of films with different defect structures, prove the strong connection between microstructure, interfaces and critical currents. Equal investigations of heterostructures to those of the superconducting films show a strong influence of the ferromagnet on the critical current. This is explained by the penetration of an inhomogeneous stray field distribution from the ferromagnet through the superconducting layer. Diese Arbeit konzentriert sich auf die Untersuchung von supraleitenden, epitaktischen Dunnfilmen aus YBCO. Im zweiten Teil wird eine ferromagnetische Schicht aus LCMO dem Supraleiter zugefugt. Alle Filme sind mittels eines magnetooptischen Verfahrens untersucht worden, welche die direkte Abbildung der kritischen Stromdichteverteilung in den Proben ermoglicht. In erster Linie wurden temperaturabhangige Messungen durchgefuhrt. Durch die Verwendung einer systematischen, quantitativen Analyse der Temperaturabhangigkeiten kritischer Strome, konnten verschiedene Verankerungsmechanismen des Flusses als strombegrenzend in verschiedenen Temperaturbereichen bestimmt werden. Vergleiche von Filmen unterschiedlicher Fehlerstruktur zeigen den starken Zusammenhang zwischen Mikrostruktur, Grenzflachen und kritischen Stromen. Untersuchungen an Heterostrukturen vergleichbar zu denen an supraleitenden Filmen, zeigen einen starken Einfluss des Ferromagneten auf die kritischen Strome. Dies konnte durch das Eindringen einer inhomogenen Streufeldverteilung der Ferromagneten durch die supraleitende Schicht erklart werden.

The variation of the transition temperature of high Tc superconductors by electric field effect

Worldwide there is an increasing need for a more sustainable form of electrical power delivery with a growing share of renewable energy generation. In the distribution and transmission network, large-scale and small-scale wind and solar power plants will be introduced, in proportion to the annual economic growth. The transmission and distribution network will be expanded, focusing on the electricity transport, however, there will also be a need for exchanges with neighboring countries. Alternative solutions are needed in order to support the changes of the future grid. High temperature superconductors are an alternative to conventional conductors, due to their high current density and very low AC loss, and therefore deserve more attention. The purpose of this study is to explore ways to integrate high-temperature superconducting cables in a future network and to compare their favorable technical properties with, e.g., the conventional XLPE cable. The development of 2nd generation high temperature superconducting tapes results in a high tape quality, making it very attractive for use in superconducting power transmission cables. At the same time, the network requirements placed on the grid, based on society needs are changing, such as low magnetic field emissions, reducing space requirements, lower losses, minimizing visual intrusion, etc. Our study shows that superconducting cables compared to conventional cables score better on these societal requirements. From our comparison of three practical low and high temperature superconductors we can conclude that Yttrium Barium Copper Oxide is the most suitable superconductor for use in transmission cables. Our techno-economic analysis shows that superconducting cables become already competitive with conventional cable in the AC transmission, such as XLPE cables. Possible future problems concerning the transport capacity in the power grid where high temperature superconducting cables can offer a solution have been identified. For one promising location, we have formulated the requirements for the design of a high-temperature superconducting cable. Next, we propose two types of cable systems (with cold and warm dielectric). For both types we describe the core, the electrical insulation, the screen, the cryostat, the cooling system, etc. Also for the distribution grid a techno-economic investigation is conducted. To assess the feasibility of the application in distribution grids, we have experimentally demonstrated a reduction of AC conductor losses from 1 W/m to 0.1 W/m. We also carried out an experimental investigation to improve the developed cryostat design for a 6 km long cable connection. Despite these substantial technical improvements our economic study showed that the high-temperature superconducting distribution cable is not yet competitive with the present conventional distribution cable systems except for niche locations where additional advantages e.g. magnetic emission, reduced space usage, power density weighs more heavily. Besides the HVAC grid the Netherlands has HVDC interconnections with neighboring countries and there are initiatives for the use of DC high voltage connections to wind farms further out to sea. In our study, we make reference to a suitable location, where the above mentioned attractive features of the superconducting cable are applicable as well. We advised a modified design of a HTS HVDC cable which enables a possible upgrade of the transmission capacity of the HVDC link at such location. The main results from the investigation are that: • Based on our techno-economic analysis HTS cables offer the most competitive solution in transmission grids. Introduction of such cables will reduce HTS tape price, which in turn will stimulate further applications. • Conceptual designs of competitive HTS AC and DC transmission cables are formulated along with that for HTS AC distribution cable. Novel designs allow for much longer length between cooling stations. • Our experimental research has shown that HTS cable core losses may be reduced by a factor 10 (down to 0.11 W/m/phase at 3 kArms, 77 K, 50 Hz). • Dedicated low friction cable cryostat was developed and successfully tested for 47 meters length. Patented multi-layer thermal insulation improves the cable cryostat heat leak from 1 W/m to 0.1 W/m.