Magneto-Josephson effects and Majorana bound states in quantum wires

Abstract

A prominent signature of Majorana bound states is the exotic Josephson effects they produce, the classic example being a fractional Josephson current with 4πperiodicity in the phase difference across the junction. Recent work established that topological insulator edges support a novel `magneto-Josephson effect', whereby a dissipationless current exhibits 4π-periodic dependence also on the relative orientation of the Zeeman fields in the two banks of the junction. Here, we explore the magneto-Josephson effect in junctions based on spin-orbit coupled quantum wires. In contrast to the topological insulator case, the periodicities of the magneto-Josephson effect no longer follow from an exact superconductor-magnetism duality of the Hamiltonian. We employ numerical calculations as well as analytical arguments to identify the domain configurations that display exotic Josephson physics for quantum-wire junctions, and elucidate the characteristic differences with the corresponding setups for topological insulators edges. To provide guidance to experiments, we also estimate the magnitude of the magneto-Josephson effects in realistic parameter regimes, and compare the Majorana-related contribution to the coexisting 2π-periodic effects emerging from non-Majorana states.

8+ pages, 8 figures, minor changes, figures added; published version

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• Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Magnetoelectric coupling in superconductor-helimagnet heterostructures
• Majorana states and magnetic orbital motion in planar hybrid nanowires
• Long Range Triplet Josephson Current and $0-\pi$ Transition in Tunable Domain Walls
• Tomography of zero-energy end modes in topological superconducting wires
• Ground-state electronic structure of quasi-one-dimensional wires in semiconductor heterostructures
• Majorana phi0 Junction in a Disordered Spin-orbit Coupling Nanowire with Tilted Magnetic Field
• Josephson current between two $p$-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields
• Effect of Magnetic Field and Rashba Spin-Orbit Interaction on the Josephson Tunneling between Superconducting Nanowires
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• A particle in equilibrium with a bath realizes worldline supersymmetry
• Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids
• Green Function Invariants for Floquet Topological Superconductivity Induced by Proximity Effects