Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

Thermal conductivity in dirty superconducting alloys in high field

This paper discusses the thermal conductivityK of a dirty type II superconductor in the mixed state, for fields close to the upper critical field (H _e2 orH _e3) where the electronic component is dominant and easily separated. To order |Δ|², the conductivity depends only on the space average 〈|Δ|²〉. Our formula is a generalisation of earlier results byMaki andAmbegaokar andGriffin for gapless superconductors. The slope\(\left( {\frac{{\partial K}}{{\partial H}}} \right)_{Hc2} \) is proportional to the slope of the magnetization curve\(\left( {\frac{{\partial K}}{{\partial H}}} \right)_{Hc2} \), the ratio of these two slopes being a universal function of temperature. These results are very different from the predictions of the “effective gap” model.     

Temperature dependence of the surface upper critical field of superconducting alloys

The temperature dependence of the surface upper critical field,H _c3, nearT _c is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveH _c3/H _c2 versust=T/T _c att=1 is found to decrease monotoneously from zero to ?1.040 as one goes from the “dirty” to the “clean” limit.     

Electronic thermal conductivity of superconducting thin films of lead-indium alloy

The thermal conductivity of thin films of superconducting Pb-3 at. % In alloy is measured in the normal and the superconducting states. The ratio of the electronic thermal conductivity in the superconducting state K_es to that in the normal state K_en is found to be in good agreement with the Bardeen, Rickayzen and Tewordt theory with 2?_O = 4.36 kT_c.     

Thermal conductivity of superconducting niobium

The phonon scattering term in the superconducting state of the electronic conduction has been obtained for niobium which is regarded as an intermediate coupling superconductor. The limiting slope for the phonon scattering term of the reduced thermal conductivity against reduced temperature has been found to be 2.8, as compared with 1.5 for weak coupling superconductors.     

Theory for the upper critical field in superconducting multilayers with interface irregularities

The upper critical field in superconducting multilayers, which are composed of two kinds of superconducting layers with different diffusion constants and contain interface irregularities, investigated in the direction parallel to the layers. The interface irregularities enhance the upper critical field. The crossover temperature at which the superconducting nucleation position moves from one layer to another is increased as the effect of the irregularities becomes strong. As a result, the two-dimensional region where the nucleation position of the superconducting order is inside a layer with the larger diffusion constant is greatly reduced by the irregularities.     

Finite width effect on the upper critical field Hc2 of superconducting networks

A recent prediction for the continuum limit of the upper critical field of infinite superconducting networks H_c2(T)= dH^(bulk)_c2 (d=spatial dimension of the network) is checked experimentally. A direct comparison of the measured critical fields on both samples: film and infinite 2D regular networks, made of the same material, support strongly this theoretical prediction. The deviation of the proportionality coefficient from d=2 is attributed to the finite width of wires. Wires of finite width are shown to be responsible for a renormalization of the diffusion coefficient of Cooper pairs. The expression so obtained for H_c2 as a function of the filling factor is consistent with the measured value.     

Thermal conductivity of superconducting tunneling junctions

We present the first measurements of thermal conductivity of superconducting tunneling junctions. Point contact junctions were established between a GaAs (Zn) point and a superconducting Nb base. We also used a dielectric tip made of GaAs (Cr).We conclude that electrons carry the heat across these type of junctions, in the same way they do in a bulk superconductor, and that the acoustical mismatch at the interface is not affected by the superconducting transition of the base metal.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Intrinsic behavior of flux lines in pure niobium near the upper critical field

We report small-angle neutron-scattering (SANS) measurements of flux line properties near H(c2) in an ultrapure sample of niobium with weak pinning of flux in the bulk. These confirm in detail the Abrikosov picture of the flux line lattice to within 20 mK of the upper critical field line. However, it has recently been claimed [X. S. Ling et al., Phys. Rev. Lett. 86, 712 (2001)], on the basis of SANS observations of a disordering of flux lines in niobium, that the flux lattice melts at temperatures clearly separated from the upper critical field line. This discrepancy may possibly arise from differences in sample purity and pinning.     

Amorphous magnetic alloys near critical concentration: Low field reversible dc magnetization

Measurements of the reversible magnetization at low dc fields have been used to investigate the magnetic response near the multicritical point (x_c) of two sets of amorphous alloys. In both cases, the ferromagnetic (FM) to spin glass (SG) transition line is found to be non-monotonic. The collapse of the magnetization as x→x⁺_c and the rapid increase in the susceptibility as x→x^-_c are suggestive of a percolation transition in the magnetic network at x=x_c. From a study of the non-linear susceptibility in the most concentrated spin glass alloy in each system, we obtain scaling exponents in agreement with previous reports providing further support for a thermodynamic phase transition at the spin glass temperature. For the first time we find a divergence in the linear susceptibility in these samples similar to that expected for the non-linear susceptibility and attribute it to their proximity to the FM phase. Dramatic changes in the transition temperatures and a perceptible shift in x_c are observed when normal boron is replaced by enriched boron (≈100%¹¹B) in one series of alloys.     

Disordered nanocrystalline superconducting PbMo6S8 with a very large upper critical field

Large increases in the upper critical field B(C2)(0) are reported in bulk superconductors that demonstrate another novel property for nanocrystalline materials. Disordered nanocrystalline PbMo6S8 superconductors were fabricated by mechanical milling and hot isostatic pressing. Conventional PbMo6S8 has B(C2)(0) approximately 50 T. The nanocrystalline materials have higher resistivity (rho(N)) and B(C2)(0) approximately 100 T. The disorder produced in these nanocrystalline materials is significantly different from that produced by doping because it increases rho(N) and, hence, B(C2)(0) without significantly reducing the electronic density of states or superconducting transition temperature (T(C)). Furthermore, the disorder reduces the electron mean-free path to approximately 1 nm which is more than an order of magnitude smaller than the grain size and necessary to achieve the unprecedented increase in B(C2)(0).     

Predicted electric field near small superconducting ellipsoids

We predict the existence of large electric fields near the surface of superconducting bodies of ellipsoidal shape of dimensions comparable to the penetration depth. The electric field is quadrupolar in nature with significant corrections from higher order multipoles. Prolate (oblate) superconducting ellipsoids are predicted to exhibit fields consistent with negative (positive) quadrupole moments, reflecting the fundamental charge asymmetry of matter.     

Thermal conductivity as a probe of unconventional superconducting gap

We have carried out a comparative study of the thermal conductivity of two rectangular single crystals: a niobium sample and a detwinned YBCO. Thermal conductivity was measured as a function of the relative orientation of the crystaline axes and a magnetic field applied parallel to the sample plane. Different angular variations, two-fold for Nb and four-fold for YBCO, were observed in the two case. We discuss the microscopic effects related to the gap structure which are at the origin of this qualitative difference in the behavior of thermal conductivity in these two superconductors.     

First-order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and T(c) is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger T(c). A second order superconducting transition emerges only at some distance from the FQCP.