Normal Layer Thickness Research Articles

Influence of intralayer quantum-well states on the giant magnetoresistance in magnetic multilayers.

A model which can account for the experimentally observed variations of the giant magnetoresistance in thin magnetic multilayers with mean free path, interface roughness, magnetic layer, and normal layer thickness has been developed. The model requires the existence of quantum-well states within individual layers or groups of layers, depending on the magnetic state of the film. The calculated results are ob tained by the application of quantum size effect transport theory to these individual layers

Transistors based on proximity effect control of the critical current of a superconductor

The critical current of a bilayer consisting of a thin superconductor in contact with a normal conductor depends on the thickness of the normal layer due to the proximity effect. Using one electrode of a semiconductor pn junction as the normal material, it is possible to vary the normal layer thickness by applying a voltage to the pn junction. The author discusses the feasibility of transistors based on such structures. He concludes that there is no fundamental impediment to operating a transistor based on proximity effect control of a superconductor. However, the proposed device requires that both superconductor and semiconductor layers be no thicker than roughly a coherence length. The large mismatch at the superconductor-semiconductor interface reduces the size of the proximity effect, possibly making the desired effect too small to be useful. It is difficult to construct a nonlatching device, or one with voltage gain. Thus, the proposed device has major drawbacks which prevent it from being considered as more than a scientific curiosity. >

Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges

The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*=∫ −L L [1−Δ(z)/Δ]dz, where Δ(z) is the pair potential of the junction, Δ is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than Δ besides the BCS peak atE=Δ; forE>Δ there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.

Andreev scattering and density of states in weakly coupled superconductors

The Bogoliubov-de Gennes Equations (BdGE) for inhomogeneous superconductors are transformed by a WKBJ ansatz into a set of two coupled nonlinear differential equations for slowly varying complex functions η(z) and ξ(z) which determine the quasiparticle wave functions. These equations are solved both numerically and in successive iterations starting from the known values of η and ξ in the homogeneous superconductor. We find that for energies above the gap the probability of Andreev scattering from a self-consistently varying pair potential Δ(z) is considerably smaller than that for a step-like pair potential. In microbridges the density of states of the bound states agrees very well with that of a rectangular pair potential well with an effective normal layer thickness ∫ [ 1 − Δ ( z ) Δ ] d z ; Δ is the constant value of Δ(z) deep in the superconducting banks. In junctions with finite S-layer thickness the density of the continuum states exhibits oscillations which are due to electron-hole interferences.

Proximity effect sandwiches containing nonmagnetic localized states

The effects of resonant scattering by nonmagnetic localized states in the normal layer on the critical temperatures of proximity effect sandwiches are studied through the renormalization of the electron propagators in the McMillan proximity effect model. By treating both the resonant scattering of the normal layer electrons and the Coulomb correlation between electrons of opposite spins located on the same impurity site self-consistently, an expression for the decrease in the critical temperature that shows explicitly the dependences on the parameters that describe the impurity atoms is obtained. The decrease in the critical temperatures as a function of impurity concentration and of normal layer thickness is shown.

Phase coherence, quantization, and thermal fluctuations in SNS junctions

Abstract Quasiparticles in the bound and continuum states of superconducting- normal-superconducting junctions are scattered by thermal fluctuations. The scattering rates are computed as functions of temperature and normal layer thickness. Phase coherence of the pair potential is broken, if more than half of the quasiparticles in the continuum states are scattered before crossing of the N-region once. For the corresponding critical quasiparticle life-time τKc (coherence time) the r.m.s. fluctuation of the phase difference 〈 χ 2 ( τ Kc )〉 1 2 is of the order of π. Except at very low temperatures the bound states are considerably more stable against thermal fluctuations than the continuum states so that even in the absence of phase coherence the size-dependent quantization of the Andreev spectrum exists for sufficiently large momenta normal to the layer boundaries.

Thickness dependence of the maximum DC Josephson current in superconducting proximity junctions

Abstract We investigated the maximum dc Josephson current I M in NbNb x O y Cu/Pb junctions as a function of normal layer thickness d Cu . Theoretical calculations based on the McMillan proximity effect model are in good agreement with the experimental data. The monotonous decrease of RI M ( R is the normal tunneling resistance) indicates the absence of any oscillatory behaviour or anomaly in the pair amplitude F Cu ( d Cu ) of the Cu/Pb sandwich, in contradiction with theoretical prediction.

Josephson Current Flow in Pure Superconducting-Normal-Superconducting Junctions

It is shown that the Josephson current in a pure superconducting-normal-superconducting (SNS) sandwich with normal layer thickness large compared with the coherence distance can be calculated easily from the quasiparticle spectrum by use of Galilean invariance. The results agree with Ishii at $T=0\ifmmode^\circ\else\textdegree\fi{}$K and with an expression of Kulik for the bound-state contribution, but we do not find a larger contribution from states with $E$ near ${\ensuremath{\Delta}}_{0}$ as suggested by Kulik. The expected current decreases very rapidly with increase in temperature so that it would be necessary to go to very low temperatures to observe the effect.