Josephson current between topological and conventional superconductors

Abstract

We study the stationary Josephson current in a junction between a topological and an ordinary (topologically trivial) superconductor. Such an S-TS junction hosts a Majorana zero mode that significantly influences the current-phase relation. The presence of the Majorana state is intimately related with the breaking of the time-reversal symmetry in the system. We derive a general expression for the supercurrent for a class of short topological junctions in terms of the normal state scattering matrix. The result is strongly asymmetric with respect to the superconducting gaps in the ordinary (${\Delta }_0$) and topological (${\Delta }_{\mathrm{top}}$) leads. We apply the general result to a simple model of a nanowire setup with strong spin-orbit coupling in an external magnetic field and proximity-induced superconductivity. The system shows parametrically strong suppression of the critical current $I_c\propto {\Delta }_{\mathrm{top}}/R_N^2$ in the tunneling limit ($R_N$ is the normal state resistance). This is in strong contrast with the Ambegaokar-Baratoff relation applicable to junctions with preserved time-reversal symmetry. We also consider the case of a generic junction with a random scattering matrix and obtain a more conventional scaling law $I_c\propto {\Delta }_{\mathrm{top}}/R_N$.

7 pages, 2 figures

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• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Finite length effect on supercurrents between trivial and topological superconductors
• Signatures of time-reversal-invariant topological superconductivity in the Josephson effect
• Transport signatures of Majorana bound states in superconducting hybrid structures
• Dynamics of hybrid junctions of Majorana wires
• Josephson effect in junctions of conventional and topological superconductors
• $6\pi$ Josephson effect in Majorana box devices
• Nonequilibrium electrical, thermal and spin transport in open quantum systems of topological superconductors, semiconductors and metals
• The influence of the Majorana non-locality on the supercurrent
• Josephson current via an isolated Majorana zero mode