Signatures of time-reversal-invariant topological superconductivity in the Josephson effect

Abstract

For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal-invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical and numerical results that hold for arbitrary normal-state conductance and the most general forms of spin-orbit coupling. The signatures of topological superconductivity we find include the fractional ac Josephson effect, which arises in topological-topological junctions provided that the energy relaxation is sufficiently slow. We also show, for both junction types, that robust signatures of topological superconductivity arise in the dc Josephson effect in the form of switches in the Josephson current due to zero-energy crossings of Andreev levels. The junction spin-orbit coupling enters the Josephson current only in the topological-topological case and in a manner determined by the switch locations, thereby allowing quantitative predictions for experiments with the normal-state conductance, the induced gaps, and the switch locations as inputs.

16 pages, 11 figures. v3: corrected typo (missing sign term in the exponent) in Eq. (7)

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Cited by in corpus (17)

• Floquet Majorana and Para-Fermions in Driven Rashba Nanowires
• Parity-controlled $2\pi$ Josephson effect mediated by Majorana Kramers pairs
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Manipulation of Cooper pair entanglement in hybrid topological Josephson junctions
• 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
• Survival of the fractional Josephson effect in time-reversal-invariant topological superconductors
• Time-reversal-invariant topological superconductivity
• Josephson junctions of 2D time-reversal invariant superconductors: signatures of the topological phase
• Spontaneous Josephson $\pi$ Junctions with Topological Superconductors
• Insulating regime of an underdamped current-biased Josephson junction supporting ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ parafermions
• Topological Josephson Junctions in the Integer Quantum Hall Regime
• Exact analytical solution of a time-reversal-invariant topological superconducting wire
• Zero-dimensional topologically nontrivial state in a superconducting quantum dot
• Fusion Rules of Majorana-Kramer-Pairs in Time-Reversal-Invariant Topological Superconductors
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors