Josephson effect in superconducting wires supporting multiple Majorana edge states

Abstract

We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy spectrum with the superconducting phase is investigated by combining numerical diagonalizations of tight-binding models describing the SNS junction together with an analysis of appropriate low-energy effective Hamiltonians. We show that the four pi-periodicity characteristic of the fractional dc Josephson effect is preserved. Additionally, the ideal conductance of a NS junction with a topological supraconductor, hosting two Majorana modes at its ends, is doubled compared to the single Majorana case. Last, we illustrate how a nonzero superconducting phase gradient can potentially destroy the phases supporting multiple Majorana end states.

9 pages, 11 figures

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• Majorana fermion exchange in strictly one dimensional structures
• Majorana Bound States in Double Nanowires with Reduced Zeeman Thresholds due to Supercurrents
• Interaction-Induced Renormalization of Tunneling into Multiple Majorana End States of a Topological Superconducting Wire
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
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• Majorana fermions in topological insulator nanowires: from single superconducting nanowires to Josephson junctions
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• Effects of Peierls phases in open linear chains
• Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes
• Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids
• Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Interfacing a topological qubit with a spin qubit in a hybrid quantum system