Theoretical Investigation of the Current–Voltage Characteristics of Superconducting Niobium–Lead Tunnel Junctions

Abstract

A proximity-effect model for the niobium electrode is presented assuming on the barrier side the existence of a thin surface layer which differs from the other part of the niobium electrode. The resulting dependence of the quasiparticle current-voltage characteristic on temperature and electrode thickness shows good agreement with experimental results.Unter der Annahme einer Oberfliichenschicht auf der Niobelektrode, die sich vom darunterliegenden Material unterscheidet, wird ein Proximityeffekt-Mode11 zur Beschreibung der Niobelektrode vorgestellt. Die damit erhaltenen Abhangigkeiten der Quasiteilchen-Strom-Spannungskennlinie von der Temperatur und der Elektrodendicke stimmen gut mit experimentellen Ergebnissen uberein.

Theoretical Investigation of the Critical Josephson Current of Niobium‐Lead Tunnel Junctions

“…I n order to explain the experimental results concerning the critical Josephson current and its temperature dependence, as a rule, the theoretical expression of AB is used We use our theoretical model of niobium-lead tunnel junctions, which has yielded good results for the current-voltage characteristics [13], and evaluate the theoretical critical current I, numerically according to (1). At first, the effect of a "truly" nornially conducting surface layer characterized by a phonon-induced gap energy AEh = 0 on the critical current is demonstrated.…”

“…I n analogy to the density of electron states which determines the quasiparticle tunneling current [13], in (1) the pair densities P and of the left (L) and right (R) electrode, respectively, can be calculated with the help of the one-electron Green's function matrix G,…”

“…I n this paper we use a proximity-effect model for niobium electrodes [13] in calculating the critical current through niobium-lead tunnel junctions. It is shown that the critical current and its temperature dependence are strongly influenced by any normal layer or superconducting surface layer with properties which differ from those of the basis niobium electrode.…”

“…Our treatment leads to a set of four nonlinear equations for the coniplex renornialization function and pair potential, which has to be solved mmierically [13]. Functions q(w) and Z ( w ) of the surface layer provide then together with equation (4) the required pair density P ( w ) of the niobium electrode.…”

“…The parameters characterizing the two parts of the niobium electrode with indices i = N and S, respectively, are the phononinduced gap energies dfh( 7') and the critical temperatures T,,, which are interrelated by ( 5 ) . The layer thicknesses d, and d, determine the coupling parameters TI, Here, vF represents the electron Fermi velocity and D denotes the average transmission probability of the interface between the two niobium electrode slabs [13].…”