Josephson effect in junctions of conventional and topological superconductors

Abstract

We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support ${\phi }_0$-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

15 pages, 9 figures, to be published in Beilstein Journal of Nanotechnology, thematic series "Topological Materials"

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Cited by in corpus (14)

• Weak measurement protocols for Majorana bound state identification
• Giant shot noise from Majorana zero modes in topological trijunctions
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Finite length effect on supercurrents between trivial and topological superconductors
• Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire
• Transport signatures of Majorana bound states in superconducting hybrid structures
• Catalogue of Andreev spectra and Josephson effects in structures with time-reversal-invariant topological superconductor wires
• Tomography of zero-energy end modes in topological superconducting wires
• The influence of the Majorana non-locality on the supercurrent
• Josephson current via an isolated Majorana zero mode
• Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• The feedback driven atomic scale Josephson microscope
• Optimal Majoranas in Mesoscopic Kitaev Chains