Suppression and enhancement of the critical current in multiterminal superconductor–normal-metal–superconductor mesoscopic structures

Abstract

We analyse the measured critical current Im in a mesoscopic 4-terminal S/N/S structure. The current through the S/N interface is shown to consist not only of the Josephson component Ic sin ϕ, but also a phase-coherent part Isg cos ϕ of the subgap current. The current Im is determined by the both components Ic and Isg, and depends in a nonmonotonic way on the voltage V between superconductors and normal reservoirs reaching a maximum at V ∼ = ∆/e. The obtained theoretical resultas are in qualitative agreement with recent experimental data.Recent achievements in nanotechnology have revived interest in the study of nonequilibrium and phase-coherent phenomena in superconductor-normal metal (S/N) structures. One of the most remarkable, discovered recently [1], was the observation of the sign reversal of the Josephson critical current I c (the so-called π-junction) in a multiterminal mesoscopic Nb/Au/Nb structure under nonequilibrium conditions. By passing an additional current through the N layer or, in another words, by applying a voltage V to the normal reservoirs (see Fig.1) with respect to the superconductors, one can create a nonequlibrium electron-hole distribution, or at least one can shift this distribution with respect to the electron-hole distribution in the superconductors. Under this condition, the critical current I c decreases with V and changes sign at a certain value of the applied voltage V . This effect was predicted first in Ref.[2] where a ballistic 3-terminal structure was considered (for more details, see also Refs. [3,4]). In diffusive 4-terminal S/N/S structures, the sign-reversal effect has been considered in Refs. [5][6][7] (see also [8,9]). The sign-reversal effect and switching of the π-junction into a state where ϕ = π has much in common with an instability of an uniform superconductor with a nonequilibrium distribution function [10,11].In multi-terminal S/N/S structures one can observe not only the sign reversal effect, but also a number of other interesting phenomena. For example, the conductance of a normal wire between N reservoirs oscillates with varying phase difference ϕ (see review articles [12,13]). In addition, as shown in Refs. [5,14], the measured critical current I m depends on the geometry of a particular structure and instead of decreasing may also increase with increasing voltage V . In particular one can observe Josephson-like effects (plateau on the I 3 (V S ) curve, oscillations of the measured critical current I m in a magnetic field etc) even if the Josephson coupling between superconductors under equilibrium conditions is negligable. The reason for these effects is that the current I m in a multi-terminal S/N/S structure is determined not only by the Josephson component I c sin ϕ, but also by the phase-dependent subgap current I sg cos ϕ through the S/N interface. Therefore even in the case of a small I c , the current I m can be altered by varying the phase φ. An increase of the critical current was observed in the recent paper [15] where a mesoscopic three-terminal ...

Influence of magnetic impurities on charge transport in diffusive-normal-metal/superconductor junctions

“…[5][6][7][8][9][10][11][12][13][14][15] The physics of ZBCP was extensively studied theoretically using scattering matrix approach [16][17][18][19][20][21] and the quasiclassical Green's function technique. 22,[25][26][27][28][29][30][31][32][33][34] Volkov, Zaitsev, and Klapwijk ͑VZK͒ 22 explained the origin of the ZBCP in DN/S junctions in the framework of the quasiclassical theory by solving the Usadel equations 23 with the Kupriyanov and Lukichev ͑KL͒ boundary condition for the Keldysh-Nambu Green's function. 24 According to the VZK theory the ZBCP is due to the enhancement of the pair amplitude in DN by the proximity effect.…”

Theory of charge transport in diffusive normal metal/conventional superconductor point contacts

“…As shown by Lambert et al 26 , this condition is exact in two limits of either high or low barrier transparency, with small corrections in the intermediate transparency range. By applying the VZK theory, several authors studied the charge transport in various junctions 27,28,29,30,31,32,33,34 by solving the Usadel equations. (see review by Belzig et al 35 ).…”

Nonequilibrium Josephson effect in short-arm diffusive SNS interferometers

“…In theoretical analysis of the interferometer effect in diffusive junctions, the presence of the Josephson current is usually ignored. Similarly, the theoretical studies of the nonequilibrium Josephson effect 17,18,19 are restricted to the regime of "weak" prox-imity effect, 9,21,22 when the induced gap in the normal bridge is much smaller than those in the superconducting reservoirs. Such a regime is relevant for long diffusive junctions and for junctions with high-resistance NS interfaces.…”