A microscopic model for the nonequilibrium proximity effect in superconductor-normal metal junctions

The current-voltage characteristics of a superconductor-normal metal junction are affected by the proximity superconductivity induced on the normal side. We study this effect using the quasiclassical theory. We first present a unified derivation of the previous results obtained by time-dependent Ginzburg-Landau (TDGL) theories. In order to study the effect beyond the scope of the TDGL theory, we approximate the induced order parameter by a step function. The amplitude and the phase of the induced order parameter as well as the width of the step are determined self-consistently. The calculation is made in the pure limit, but no restrictions are set on the temperature or on the transmission coefficient of the junction besides the ones implicit in the step approximation. A time-dependent solution for the order parameter is found at all currents or voltages. It is found that the results in the TDGL region and outside are relatively similar, although different mechanisms are responsible for the conversion from the normal to supercurrent in each case.     

The dc Josephson effect for superconducting proximity Kondo alloys

We calculate the maximum dc Josephson current I _Mof S-I-NX/S tunnel junctions, where N is a normal metal containing a low concentration c of magnetic impurities X in proximity with a superconducting film S. Our calculation shows a reentrant behavior of I _Mvs temperature T. A three-dimensional representation of f(I_M; T; c) = 0 is given.Laboratoire associé au CNRS.Research fellow of the Belgian IIKW.     

Isotope effect in the hubbard model for d-wave superconductivity

We have solved the generalized Eliashberg equations for the 2D Hubbard model with interactions due to exchange of antiferromagnetic spin fluctuations and harmonic phonons. We calculate the supression of T_c for d-wave superconductivity, the isotope exponent , and the resitivity with different models for the phonon interaction ²F(q, ). The smallest T_c supression and the largest values are obtained for interactions which are enhanced atq = 0. At lower temperatures the spin-fluctuation interaction is strongly reduced by the phonon interaction due to feed-back effects. We compare our results with the experimental data on high-T_c superconductors.     

Crystallization-induced superconductivity in amorphous Ti-Ta-Si alloys

Amorphous alloys containing 0 to 40 at% Ta and 15 to 20 at% Si have been produced in the ternary Ti-Ta-Si system by rapidly quenching the melts using a melt-spinning technique. The amorphous alloys did not show any superconducting transition down to liquid helium temperature (4.2 K). However, a transition was detected above 4.2 K after inducing crystallization in these alloys by annealing at appropriate temperatures. The superconducting transition temperature, T _c, increased with increasing tantalum content and showed the highest value of 7.6 K for the Ti₄₅Ta₄₀Si₁₅ alloy annealed for 1 h at 1073 K. An upper critical magnetic field, H _c2 of 4.7×10⁶ Am^–1 at 4.2 K and a critical current density, J _c, of 1.5×10⁴ A cm^–2 at zero applied field and 4.2 K were recorded for this alloy. Detailed electron microscopic studies of the crystallization behaviour of the amorphous alloys established that a supersaturated solid solution of tantalum in -Ti with a bcc structure forms first, followed by the precipitation of the bc tetragonal Ta₃Si compound. Since Ta₃Si is not superconducting above 4.2 K, it has been concluded that superconductivity in the crystallized alloys is due to the precipitation of -Ti(Ta) solid solution.     

The martensitic transformation in uranium metal and its effect on superconductivity

• 1.1.) I propose that the superconducting transition temperature (T_c) of uranium metal is affected by the degree of completion of the α-U → α′-U martensitic (displacive) transformation and that the superconducting behavior must therefore respond to factors found to be important with high-T_c materials.
• 2.2.) It is suggested that the effects of impurities on phase stability and a variable low-temperature martensitic transformation can be explained by a combination of three theories: VELD theory (21), McMillan's Landau theory (8) and Roitburd's domain theory (10).
• 3.3.) It is proposed that there may be more than one incommensurate CDW state in the pre-martensitic temperature range of α-phase U.
• 4.4.) The observed superconducting transition temperature of uranium appears to depend upon whether the structure is commensurate or incommensurate at T_c.
• 5.5.) It is explained how factors affecting the variable T_c can be responsible for the anomalous thermal properties of U.

     

On the proximity effect in a superconductive slab bordered by metal

The first Ginzburg-Landau equation for the order parameter in the absence of magnetic fields is solved analytically for a superconducting slab of thickness 2d bordered by semi-infinite regions of normal metal at each face. The real-valued normalized wave function f=/ depends only on the transversal spatial coordinate x, normalized with respect to the coherence length of the superconductor, provided the de Gennes boundary condition df/dx=f/b is used. The closed-form solution expresses x as an elliptic integral of f, depending on the normalized parameters d and b. It is predicted theoretically that, for b< and dd_c=arctan(1/b), the proximity effect is so strong that the superconductivity is completely suppressed. In fact, in this case, the first Ginzburg-Landau equation possesses only the trivial solution f0.     

A Shiba-Rusinov theory for paramagnetic impurities in proximity effect sandwiches

The Shiba-Rusinov theory, which takes into account both the potential and exchange interactions existing between a conduction electron and a paramagnetic impurity atom, is used to study the effects due to paramagnetic impurities dissolved in the normal layer of a proximity effect sandwich. Using aT-matrix approach to treat the interactions due to the impurities and the standard Born approximation to treat the other interactions in the sandwich, we obtain a set of self-consistent equations for the renormalized frequencies and the unrenormalized energy gaps for the electrons in both layers. The solutions of these equations are then used to obtain expressions for the decrease in the transition temperature of the sandwich and for the jump in the specific heat atT _c .     

Nanoscale superconductor-magnetic metal structures: Critical current enhancement and proximity effect

We focus on some aspects of proximity effect in coupled superconductor-magnetic metal artificial structures and discuss mechanisms that may enhance superconductivity of such systems. Superconductor-ferromagnet tunnel junctions are considered where an inversion/enhancement of the Josephson current is due to magnetic proximity effect. Special attention has been paid to another way of enhancing superconductivity of a proximity coupled superconductor-magnetic metal system—the field-induced enhancement. This mechanism can be realized if the effective exchange field between the conducting electrons and localized spins of magnetic ions in a magnetic spacer can counteract the effect of an external magnetic field, i.e., an enhancement due to the so-called Jaccarino-Peter compensation effect.     

A new process for atomization of metal alloys

A laboratory apparatus was constructed to atomize metal alloys by forcing them through sintered ceramic disc filters. The process combines filtration of oxides and/or undesirable second phase particles with atomization. Sintered Al₂O₃ and SiO₂ disc filters with average pore sizes in the range of 36 to 150 m were used. The effectiveness of various filters in removing synthetic inclusions from Al-Ti-B melts was studied. 2 to 10 m size TiB₂ particles were successfully filtered out. Atomization experiments were done with pure aluminium and 7075 aluminium alloy. Spherical powders, 150 to 2000 m in size, of 7075 aluminium alloy with secondary dendrite arm spacings between 4 to 8 m, were cold compacted and extruded into a billet. Room temperature longitudinal properties of the billet in T6 condition were: YS 80×10³ psi, UTS 94.3×10³ psi, elongation 15% and R.A. 42%.     

V-Nb-Mo-Al-Ga高熵合金的多晶型性与超导性

高熵合金具有结构多晶型性和超导性,是当前研究的重点.然而,多晶型转变仅在非超导的高熵合金中被观察到,且大多是在高压条件下.本文报道了(V0.5Nb0.5)3-xMoxAl0.5Ga0.5(0.2≤x≤1.4)高熵合金中的超导和温度驱动多晶型性.实验结果表明当x=0.2时铸态高熵合金具有单一的体心立方(bcc)结构,而当x值更高时则为bcc和A15的混合结构.经高温退火后,bcc结构向A15结构进行多晶型转变,且所有高熵合金均表现出块体超导电性.对于x=0.2的组分,其bcc晶型直到1.8 K仍不具备超导性,但其A15晶型却在10.2 K表现出超导性,估算零温上临界磁场Bc2(0)为20.1 T,该超导温度(Tc)和磁场强度在已知的高熵合金超导体中均为最高.随着Mo含量x的增加,A15型高熵合金的Tc和Bc2(0)均降低,但Bc2(0)/Tc比值表明在宽的x范围内存在无序诱导的上临界磁场增加.Tc的降低归因于电子比热系数和电声子耦合强度的减小.此外,该高熵合金的Tc对价电子数依赖关系与二元A15超导体和其他结构高熵合金超导体均不同,且表明可以通过降低价电子数目来进一步提高Tc.本文不仅揭示了一类新结构类型的高熵合金超导体,而且提供了高熵合金中依赖于多晶型性超导的首个示例.     

Generalized McMillan tunneling model of the superconducting proximity effect

We have extended the McMillan tunneling model (MTM) of the superconducting proximity effect to the case of strongly coupled normal-superconducting composites. The generalization has been carried out by treating the tunneling Hamiltonian to all orders of self-consistent perturbation theory. The electronic density of states, the real and imaginary parts of the order parameter, the energy gap, and the transition temperatureT _c calculated in the generalized model are significantly different from the MTM results. Generally, the peak inN _N (E) is broader, shifted, and damped. The energy gap is lower and the depression inT _c is softened.Work supported in part by a grant from the National Research Council of Canada.     

Empirical model for the estimation of thermophysical properties of liquid metal alloys

A model for calculating the main properties of liquid metal binary alloys at standard pressure based on experimental data observation is presented. Given the characteristics of the pure metals, the model allows to calculate density, surface tension, electrical resistivity and thermal conductivity of binary alloys at various concentrations along the liquidus line. Some preliminary comparisons for Al-Si and Al-Cu systems are in satisfactory agreement with the model.     

A three-dimensional model for particle dissolution in binary alloys

A three-dimensional model for particle dissolution in binary alloys is proposed and its numerical solution procedure is described. The model describes dissolution of a stoichiometric particle as a Stefan problem. The numerical method is based on a level set method, which has a wide applicability in modeling moving boundary problems. The present model relies on local thermodynamic equilibrium on the interface between the dissolving particle and the diffusive phase. The level set method is shown to handle complex topological changes in particle break-up very well. The potential of the technique is demonstrated in describing the globularization of planar, perturbed and cracked cementite plates in a pearlitic microstructure.     

Theoretical study of superconductivity in MgB2 and its alloys

Using density-functional-based methods, we have studied the fully-relaxed, fulltronic structure of the newly discovered superconductor, MgB ₂, and BeB₂, NaB₂ and AlB₂. Our results, described in terms of (i) total density of states (DOS) and (ii) the partial DOS around the Fermi energy, E_F, clearly show the importance of B p-electrons for superconductivity. For BeB₂ and NaB₂, our results indicate qualitative similarities but significant quantitative differences in their electronic structure due to differences in the number of valence electrons and the lattice constantsa andc. We have also studied Mg _1-xM_xB₂ (M = Al, Li or Zn) alloys using coherent-potential to describe disorder, Gaspari-Gyorffy approach to evaluate electron-phonon coupling, and Allen-Dynes equation to calculate the superconducting transition temperature, T_c. We find that in Mg_1-xM_xB₂ alloys (i) the way Tc changes depends on the location of the added/modified k-resolved states on the Fermi surface and (ii) the variation of Tc as a function of concentration is dictated by the Bp DOS.     

Anisotropic superconductivity in the Emery model

We have investigated anisotropic superconductivity originating from intersite pairing between holes in nearest and next nearest neighboring sites in the Emery model. Strong local Coulomb correlations among holes in copper orbitals have been taken into account within the Hubbard I approximation scheme. The superconducting transition temperature has been evaluated as a function of the hole concentration. It has been shown that with the onset of superconductivity, pairing among oxygen-like quasiparticles in the mixeds-wave+d-wave channel plays the dominating role, being replaced by pairing in the extendeds-wave channel for higher concentration of holes. Superconducting correlations are mostly effective for a rather narrow range of the model parameter values, close to values derived from band structure calculations. Therefore, the coupling betweens-wave andd-wave channels seems to be a general feature of superconductivity in CuO₂ planes.     

A study of orthorhombic phases in aluminium-transition metal alloys

In recent decades some complex crystalline phases, as also many rational approximants to quasicrystalline phases with rather large unit cells, have been reported with orthorhombic symmetry in aluminium-transition metal (Al-TM) alloys. Furthermore, quite a few quasicrystalline phases, icosahedral as well as decagonal, forming in Al-TM alloys on normal or rapid solidification have been interpreted during the last decade as multiply-twinned orthorhombic crystals growing as superstructures of an orthorhombic cell that forms through welding in three perpendicular directions in the liquid state of 13-atom icosahedral clusters. Following exemplification of this new approach to quasicrystals based on the analysis of the Debye-Scherrer diffraction data from the comparatively defect-free Al-Cu-Fe icosahedral phase, the three types of orthorhombic phases in aluminium-rich Al-TM alloys, numbering 36 in all, have been examined as icosahedral cluster compounds nucleating from icosahedral atomic clusters present in the molten alloys. A detailed analysis of their lattice parameters supports the postulate that all such phases can be viewed as complex and, occasionally, as very large superstructures of a small basic orthorhombic cell. Dedicated to the dearly cherished memory of Professor Sir William Hume-Rothery F.R.S. (1899–1968) in his birth centenary year.     

Josephson effect in high-T c superconductivity

In this report we present the most important results of our recent analysis (Kupriyanov and Likharev 1990) of the Josephson effect in both the natural (intergrain) and artificial junctions using high-T _c superconductors (HTS). A comparison of the experimental data with the BCS-based theories of the Josephson effect in various tunnel-junction-type and weak-link-type structures has been carried out. The main conclusion is that the data presently available do not enable one to either confirm or reject the theories, and thus to reveal possible deviations of the real microscopic mechanism of the high-T _c superconductivity from the BCS mechanism. We suggest several experiments which would be more fruitful for this purpose, as well as for finding ways of reproducible fabrication of practically useful Josephson junctions. This work was supported by the Soviet Scientific Council on the high-Tc superconductivity problem (Grant No.42). Invited talk at the International Conference on Superconductivity, Bangalore, January 1990.     

A multi-dimensional constitutive model for shape memory alloys

This paper presents a multi-dimensional thermomechanical constitutive model for shape memory alloys (SMAs). This constitutive relation is based upon a combination of both micromechanics and macromechanics. The martensite fraction is introduced as a variable in this model to reflect the martensitic transformation that determines the unique characteristics of shape memory alloys. This constitutive relation can be used to study the complex behavior associated with 2-D and 3-D SMA structures. A simple example using this constitutive model is also presented, which reveals a new and interesting phenomenon of 3-D SMA structures.     

A simple model for crack growth in creep resistant alloys

A simple model of creep crack growth, valid for creep-resistant alloys, is described. For such alloys, it may be assumed that the creep deformation is essentially confined to a thin region in the neighborhood of the crack tip. This thin region is modeled as a cohesive zone. Outside the cohesive zone, linear elastic conditions are assumed to prevail. Numerical results for both transient and steady-state crack growth are presented. For reasonable choices of model parameters, the numerical results show rather good agreement with experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.     

A system for measurement of domain wall motion in amorphous rareearth-transition metal alloys

A system has been developed for measuring domain-wall motion in amorphous rare-earth-transition-metal alloys. A one-dimensional scanning technique is utilized in which a focused, oscillating HeNe laser spot moves over the magnetization pattern in the film. Domain walls are detected through the polar Kerr effect as the spot scans the film. A magnetic field is applied to the film in order to move the domain walls. The maximum line-scanning rate is about 250 Hz. The spot diameter at a 632.8-nm wavelength is limited to about 8 μm by the 0.46 numerical aperture of the focusing objective, the beam waist of the laser, and aberrations. The domain wall position can be measured to within ±1 μm. The apparatus is described, and the results domain-wall-motion measurements are presented