Supercurrent tunneling between conventional and unconventional superconductors: A Ginzburg-Landau approach

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Abstract
We investigate the Josephson tunneling between a conventional and an unconventional superconductor via a Ginzburg-Landau theory. This approach allows us to write down the general form of the Josephson coupling between the two superconductors, and to see which terms are forbidden or allowed by spatial symmetries. The time-reversal symmetry is also considered. We discuss the current-phase relationships, magnetic, and ac effects if we just include this direct coupling to the unconventional superconductor. In addition we consider the Josephson coupling between two short-coherence-length superconductors, extending the work of Deutscher and Müller (DM) to a finite-current calculation. We find that the critical current is suppressed below the DM value due to the fact that the coupling between the two superconductors across the junction depends on the phase difference and hence the current itself. Finally we investigate the possibility of the proximity effect, in particular the possibility that the conventional-type pairing is induced and hence coexists with the unconventional pairing near the junction. This would give the dominant contribution to the tunneling current if the direct tunneling to the unconventional pairs are suppressed for some reason. We point out that there is no possibility of dissipationless tunneling above the transition temperature of the unconventional superconductor. Even in the case in which the unconventional superconductor is below its transition temperature, we find that, for the possibility of a dissipationless current, it is crucial to have a coupling between the induced s wave and the unconventional superconductor that depends on their phase difference, which allows the conversion of the supercurrent from one type to the other. The behavior of this current, in particular as a function of temperature, is discussed. We also discuss the magnetic and time-dependent effects of the junction in the presence of this proximity effect. We see that, while some of these remain unaffected, some, in particular the time-dependent processes, are affected in a rather nontrivial manner.

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