Josephson current between topological and conventional superconductors

P. A. Ioselevich; P. M. Ostrovsky; M. V. Feigel'man

doi:10.1103/PhysRevB.93.125435

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Josephson current between topological and conventional superconductors

P. A. Ioselevich, P. M. Ostrovsky, M. V. Feigel'man

DOI 10.1103/PhysRevB.93.125435 · Physical Review B

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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 (Δ0) and topological (Δtop) 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 Ic∝Δtop/RN2 in the tunneling limit (RN 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 Ic∝Δtop/RN.