Current-Phase Relations in Superconducting Bridges

Abstract

Since p is about fc 0 (H 2 k 0 2 /2m = e F , the Fermi energy), and k <o) p /v 0 is of the order of 10 8 cm"" 1 , the condition holds, so that plasmons may decay and transfer their energy to electrons. Therefore groups of electrons originating from plasmon decay may occur in secondary electron emission spectra, since the plasmon energy ffoOp is very large compared with the single-particle energy Kkv QO The details of the rapid analyzer, experimental procedure, and results concerning the abovementioned sample materials will be published as soon as possible.I am indebted to Professor Dr. O. Glemser for many useful discussions.In a recent experiment Simmonds and Parker 1 measured the current-voltage {I-V) characteristic of a superconducting weak link comprising a Sn thin-film constriction, or Anderson-Dayem bridge. 2 Their measurements were conducted near the critical temperature T c of Sn. In this region the critical currents of the bridges are small enough so that thermal noise is expected to influence markedly the shape of the I-V curve. Their results were compared with Ambegaokar and Halperin's 3 theoretical prediction of the shape of the I-V curve for a resistively shunted, zero-capacitance Josephson tunnel junction 4 in the presence of thermal noise.A fundamental but unknown parameter in this comparison is the shape of the current-phase relation I s (cp), which relates the magnitude of the supercurrent flow in the bridge to the phase difference between the order parameters of the superconductors connected by the bridge. Simmonds and Parker used as model I s (<p) both the sinusoid appropriate to Josephson junctions and a sawtooth, the latter providing a somewhat bet-*Do Bohm and D.ter fit to their data. It is not obvious, however, that such bridges necessarily possess a continuous, single-valued I s (<p) after the manner of Josephson junctions. 5 For example the phase difference required to increase the supercurrent to its maximum, 7 C , could exceed ir, corresponding to an effectively multivalued current-phase relation. Such a situation is compatible with the observed ac Josephson behavior and with the vortexflow picture of phase slippage of Anderson and Dayem. 2 In the absence of a definite knowledge of the shape of I s (cp) the interpretation of results of experiments on the weak-link properties of bridges, e.g. that of Simmonds and Parker, 1 or, say, on electromagnetic radiation response 2 * 6 must be somewhat tentative.To resolve this question we have investigated experimentally the shape of I s (<p) for Anderson-Dayem bridges. The experiment involves measuring the dependence on applied magnetic field B of the critical current I c of a quantum interferometer 7 comprising two bridges in parallel. We sketch here how one may gain information CURRENT-PHASE RELATIONS IN SUPERCONDUCTING BRIDGESThe cur rent-phase relation I S (<P) for an Anderson-Dayem bridge is investigated making experimental use of the quantum interference between two such bridges. Near T c and for critical currents ~10 fxA 9 I J(p) is found t...

Static properties of two- and three-dimensional superconducting constrictions

“…0 is still explicitly present in the last term of Eq. (12). However, for small A this term is small except for [TI close to 7r/2 when cos -2 y is large.…”

“…On this basis, the Ginzburg-Landau equation to be solved is dEg . 12 3 AE( coshz "0 -sin2 0)(g 3-g) = 0 (17) d'r/2 g The same discussion applies as regards the importance of the last term as for three-dimensional constrictions. Even for very small A, sufficiently far from the neck A 2 cosh 2 r/ is large enough to dominate the equation, leading to g = 1 for large r/.…”

“…Omitting the last term in fact leads to the necessity of imposing rigid boundary conditions. Equation (12) shows that it has not been possible to contain all 0 dependence implicitly in the current parameter J3 and by doing so break the constriction up into separate parallel channels. 0 is still explicitly present in the last term of Eq.…”

“…Equation (12) has been solved numerically. At first our calculations were performed on an analog computer.…”

“…In elliptic cylinder coordinates VEg is equal to a-2(cosh 2r/-sin 2 0) -1 dEg/d, 12. On this basis, the Ginzburg-Landau equation to be solved is dEg .…”