Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes

We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a one-dimensional p-wave superconductor: those involving (i) longer-range hopping and superconductivity and (ii) inhomogeneous potentials. We commence with a pedagogical review of the spinless model and, as a means of characterizing topological phases exhibited by the systems studied here, we introduce bulk topological invariants as well as those derived from an explicit consideration of boundary modes. In time-reversal symmetric systems, we find that the longer range hopping leads to topological phases characterized by multiple Majorana modes. In particular, we investigate a spin model that respects a duality and maps to a fermionic model with multiple Majorana modes; we highlight the connection between these topological phases and the broken symmetry phases in the original spin model. In the presence of time-reversal symmetry breaking terms, we show that the topological phase diagram is characterized by an extended gapless regime. For the case of inhomogeneous potentials, we explore phase diagrams of periodic, quasiperiodic, and disordered systems. We present a detailed mapping between normal state localization properties of such systems and the topological phases of the corresponding superconducting systems. This powerful tool allows us to leverage the analyses of Hofstadter's butterfly and the vast literature on Anderson localization to the question of Majorana modes in superconducting quasiperiodic and disordered systems, respectively. We briefly touch upon the synergistic effects that can be expected in cases where long-range hopping and disorder are both present.

Experimental studies of the quench behaviour of MgB2 superconducting wires for fault current limiter applications

Various MgB2 wires with different sheath materials provided by Hyper Tech Research Inc., have been tested in the superconducting fault current limiter (SFCL) desktop tester at 24-26K in a self-field. Samples 1 and 2 are similarly fabricated monofilamentary MgB2 wires with a sheath of CuNi, except that sample 2 is doped with SiC and Mg addition. Sample 3 is a CuNi sheathed multifilamentary wire with Cu stabilization and Mg addition. All the samples with Nb barriers have the same diameter of 0.83mm and superconducting fractions ranging from 15% to 27% of the total cross section. They were heat-treated at temperatures of 700 °C for a hold time of 20-40min. Current limiting properties of MgB2 wires subjected to pulse overcurrents have been experimentally investigated in an AC environment in the self-field at 50Hz. The quench currents extracted from the pulse measurements were in a range of 200-328A for different samples, corresponding to an average engineering critical current density (Je) of around 4.8 × 10 4Acm-2 at 25K in the self-field, based on the 1νVcm-1 criterion. This work is intended to compare the quench behaviour in the Nb-barrier monofilamentary and multifilamentary MgB2 wires with CuNi and Cu/CuNi sheaths. The experimental results can be applied to the design of fault current limiter applications based on MgB2 wires. © IOP Publishing Ltd.

Continuous production of Bi-2212 thick film on silver tape

Bi-2212 thick film on silver tapes are seen as a simple and low cost alternative to high temperature superconducting wires produced by the Powder In Thbe (PIT) technique, particularly in react and wind applications. A rig for the continuous production of Bi-2212 tapes for use in react and wind component manufacture has been developed and commissioned. The rig consists of several sections, each fully automatic, for task specific duties in the production of HTS tape. The major sections are: tape coating, sintering and annealing. High temperature superconducting tapes with engineering critical current densities of 10 kA/cm2 (77 K, self field), and lengths of up to 100 m have been produced using the rig. Properties of the finished tape are discussed and results are presented for current density versus bend radius and applied strain. Depending on tape content and thickness, irreversible strain tirrm varies between 0.04 and 0.1 %. Cyclic bending tests when applied strain does not exceed Eirrm showed negligible reduction in J c along the length of the tape.

A device to investigate the axial strain dependence of the critical current density in superconductors

We have developed an instrument to study the behavior of the critical current density (J(c)) in superconducting wires and tapes as a function of field (mu(0)H), temperature (T), and axial applied strain (epsilon(a)). The apparatus is an improvement of similar devices that have been successfully used in our institute for over a decade. It encompasses specific advantages such as a simple sample layout, a well defined and homogeneous strain application, the possibility of investigating large compressive strains and the option of simple temperature variation, while improving the main drawback in our previous systems by increasing the investigated sample length by approximately a factor of 10. The increase in length is achieved via a design change from a straight beam section to an initially curved beam, placed perpendicular to the applied field axis in the limited diameter of a high field magnet bore. This article describes in detail the mechanical design of the device and its calibrations. Additionally initial J(c)(epsilon(a)) data, measured at liquid helium temperature, are presented for a bronze processed and for a powder-in-tube Nb3Sn superconducting wire. Comparisons are made with earlier characterizations, indicating consistent behavior of the instrument. The improved voltage resolution, resulting from the increased sample length, enables J(c) determinations at an electric field criterion E-c=10 muV/m, which is substantially lower than a criterion of E-c=100 muV/m which was possible in our previous systems. (C) 2004 American Institute of Physics.

Fabricação e caracterização de fios supercondutores do sistema BSCCO pelo método Powder-In-Tube (PIT)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joint has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Finally, a preliminary numerical study by means of Finite Element Method (FEM) of the mechanical behavior of the joints between commercial HTS is presented.

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joints has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Additionally, fatigue tests under constant cyclic stress and loading-unloading ramps have been carried out in order to evaluate the electromechanical behavior of the joints and the effect of maximum applied stress on the critical current. Finally, a preliminary numerical study by means of the Finite Element Method (FEM) of the electromechanical behavior of the joints between commercial HTS is presented.

Characterization of superconducting BSCCO/CaSiO3 and BSCCO/CaZrO3 Ag PIT wires

The addition of two compounds, calcium silicate and calcium zirconate was tested in the preparation of Bi: 2212 silver sheathed wires by powder-in-tube method. The wires were treated in an atmosphere of O-2/Ar using partial melting method. The characterizations were structural and on their electrical and magnetic properties. It was found that the addition of calcium silicate or zirconate promoted higher transition temperatures, up to 116 K for BSCCO with 1wt.% CaSiO3. The critical current densities determined by transport and magnetization measurements were improved in comparison with the wires without any addition.

Characterization of superconducting BSCCO/CaSiO3 and BSCCO/CaZrO3 Ag PIT wires

The addition of two compounds, calcium silicate and calcium zirconate was tested, in the preparation of Bi: 2212 silver sheathed wires by powder-in-tube method, which were successfully tested previously in processing chips. The wires were treated in an atmosphere of O2/Ar using partial melting method. The characterizations were structural and on their electrical and magnetic properties. As the results, transition temperatures were higher than the expected for this stage, ranged from 105K (BSCCO880) to 116K (+Si883). The critical current densities encountered in transport and magnetization measurements were improved in comparison with the wires without addition.

Binder effect on microstructure and properties of YBa2Cu3O7-x extruded wires

YBa2Cu3O7-x wires have been extruded with 2 and 5 wt.% of hydroxy propyl methylcellulose (HPMC) as binder. Both sets of wires sintered below 930°C have equiaxed grains while the wires sintered above this temperature have elongated grains. In the temperature range which gives equiaxed grains, the wires extruded with 5 wt.% HPMC have higher grain size and density. Cracks along the grain boundaries are often observed in the wires having elongated grains. Critical current density, Jc, increases initially, reaches a peak and then decreases with the sintering temperature. The sintering temperature giving a peak in Jc strongly depends on the heat treatment scheme for the wires extruded with 5 wt.% HPMC. TEM studies show that defective layers are formed along grain boundaries for the wires extruded with 5 wt.% HPMC after 5 h oxygenation. After 55 h oxygenation, the defective layers become more localised and grain boundaries adopt an overall cleaner appearance. Densification with equiaxed grains and clean grain boundaries produces the highest Jc's for polycrystalline YBa2Cu3O7 wires.

Melt-textured YBa2Cu3O7-x wires having plate-like grains

YBCO wires which consist of well oriented plate-like fine grains are fabricated using a moving furnace to achieve higher mechanical strength. Melt-texturing experiments have been undertaken on YBCO wires with two different compositions: YBa1.5Cu2.9O7-x, and YBa1.8Cu3.0O7-x. Wires are extruded from a mixture of precursor powders (formed by a coprecipitation process) then textured by firing in a moving furnace. Size of secondary phases such as barium cuprate and copper oxide, and overall composition of the sample affect the orientation of the fine grains. At zero magnetic field, the YBa1.5Cu2.9O7-x wire shows the highest critical current density of 1,450 Acm-2 and 8,770 Acm-2 at 77K and 4.2K, respectively. At 1 T, critical current densities of 30 Acm-2 and 200 Acm-2, respectively, are obtained at 77K and 4.2K. Magnetisation curves are also obtained for one sample to evaluate critical current density using the Bean model. Analysis of the microstructure indicates that the starting composition of the green body significantly affects the achievement of grain alignment via melt-texturing processes.