Theory of supercurrent transport in SIsFS Josephson junctions

Abstract

We present the results of a theoretical study of current-phase relations (CPRs) ${J}_{S}(\ensuremath{\varphi})$ in Josephson junctions of SIsFS type, where S is a bulk superconductor and IsF is a complex weak link consisting of a superconducting film s, a metallic ferromagnet F, and an insulating barrier I. At temperatures close to critical, $T\ensuremath{\lesssim}{T}_{C}$, calculations are performed analytically in the frame of the Ginsburg-Landau equations. At low temperatures a numerical method is developed to solve self-consistently the Usadel equations in the structure. We demonstrate that SIsFS junctions have several distinct regimes of supercurrent transport and we examine spatial distributions of the pair potential across the structure in different regimes. We study the crossover between these regimes, which is caused by shifting the location of a weak link from the tunnel barrier I to the F layer. We show that strong deviations of the CPR from sinusoidal shape occur even in the vicinity of ${T}_{C}$, and these deviations are strongest in the crossover regime. We demonstrate the existence of temperature-induced crossover between 0 and $\ensuremath{\pi}$ states in the contact and show that the smoothness of this transition strongly depends on the CPR shape.