Year: 2016
Type: article
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 $({\mathrm{\ensuremath{\Delta}}}_{0})$ and topological $({\mathrm{\ensuremath{\Delta}}}_{\mathrm{top}})$ 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 ${I}_{c}\ensuremath{\propto}{\mathrm{\ensuremath{\Delta}}}_{\mathrm{top}}/{R}_{N}^{2}$ 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 ${I}_{c}\ensuremath{\propto}{\mathrm{\ensuremath{\Delta}}}_{\mathrm{top}}/{R}_{N}$.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Russian Science Foundation
Award: G2499329082
OpenAlex ID: W2241236041