Quantitative Simulation of the Superconducting Proximity Effect

A numerical method is developed to calculate the transition temperature of double or multi-layers consisting of films of super- and normal conductors. The approach is based on a dynamic interpretation of Gorkov's linear gap equation and is very flexible. The mean free path of the different metals, transmission through the interface, ratio of specular reflection to diffusive scattering at the surfaces, and fraction of diffusive scattering at the interface can be included. Furthermore it is possible to vary the mean free path and the BCS interaction NV in the vicinity of the interface. The numerical results show that the normalized initial slope of an SN double layer is independent of almost all film parameters except the ratio of the density of states. There are only very few experimental investigations of this initial slope and they consist of Pb/Nn double layers (Nn stands for a normal metal). Surprisingly the coefficient of the initial slope in these experiments is of the order or less than 2 while the (weak coupling) theory predicts a value of about 4.5. This discrepancy has not been recognized in the past. The autor suggests that it is due to strong coupling behavior of Pb in the double layers. The strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for the coefficient. This agrees much better with the few experimental results that are available. PACS: 74.45.+r, 74.62.-c, 74.20.F

Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings

Granular packings slowly driven towards their instability threshold are studied using a digital imaging technique as well as a nonlinear acoustic method. The former method allows us to study grain rearrangements on the surface during the tilting and the latter enables to selectively probe the modifications of the weak-contact fraction in the material bulk. Gradual ageing of both the surface activity and the weak-contact reconfigurations is observed as a result of repeated tilt cycles up to a given angle smaller than the angle of avalanche. For an aged configuration reached after several consecutive tilt cycles, abrupt resumption of the on-surface activity and of the weak-contact rearrangements occurs when the packing is subsequently inclined beyond the previous maximal tilting angle. This behavior is compared with literature results from numerical simulations of inclined 2D packings. It is also found that the aged weak-contact configurations exhibit spontaneous restoration towards the initial state if the packing remains at rest for tens of minutes. When the packing is titled forth and back between zero and near-critical angles, instead of ageing, the weak-contact configuration exhibits "internal weak-contact avalanches" in the vicinity of both the near-critical and zero angles. By contrast, the stronger-contact skeleton remains stable

Severe discrepancies between experiment and theory in the superconducting proximity effect

The superconducting proximity effect is investigated for SN double layers in a regime where the resulting transition temperature T_{c} does not depend on the mean free paths of the films and, within limits, not on the transparency of the interface. This regime includes the thin film limit and the normalized initial slope S_{sn}= (d_{s}/T_{s})|dT_{c}/dd_{n}|. The experimental results for T_{c} are compared with a numerical simulation which was recently developed in our group. The results for the SN double layers can be devided into three groups: (i) When N = Cu, Ag, Au, Mg a disagreement between experiment and theory by a factor of the order of three is observed, (ii) When N = Cd, Zn, Al the disagreement between experiment and theory is reduced to a factor of about 1.5, (iii) When N = In, Sn a reasonably good agreement between experiment and theory is observed

Shadow on the wall cast by an Abrikosov vortex

At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadow-like region extending from the vortex to the boundary. This effect is stable for different models of the single Abrikosov vortex, for different mean free paths and also for different distances between the vortex center and the boundary. This observation promises to have also a substantial influence on the differential conductance and the tunneling characteristics for low excitation energies.Comment: 5 pages, 5 figure

A Discrete Version of the Inverse Scattering Problem and the J-matrix Method

The problem of the Hamiltonian matrix in the oscillator and Laguerre basis construction from the S-matrix is treated in the context of the algebraic analogue of the Marchenko method.Comment: 11 pages. The Laguerre basis case is adde