Energy spectrum and current-phase relation of a nanowire Josephson junction close to the topological transition

Abstract

A semiconducting nanowire proximitized by an $s$-wave superconductor can be tuned into a topological state by an applied magnetic field. This quantum phase transition is marked by the emergence of Majorana zero modes at the ends of the wire. The fusion of Majorana modes at a junction between two nanowires results in a $4\pi$-periodic Josephson effect. We elucidate how the $4\pi$-periodicity arises across the topological phase transition in a highly-transparent short nanowire junction. Owing to a high transmission coefficient, Majorana zero modes coming from different wires are strongly coupled, with an energy scale set by the proximity-induced, field-independent pairing potential. At the same time, the topological spectral gap---defined by competition between superconducting correlations and Zeeman splitting---becomes narrow in the vicinity of the transition point. The resulting hybridization of the fused Majorana states with the spectral continuum strongly affects the electron density of states at the junction and its Josephson energy. We study the manifestations of this hybridization in the energy spectrum and phase dependence of the Josephson current. We pinpoint the experimentally observable signatures of the topological phase transition, focusing on junctions with weak backscattering.

arXiv comment26 pages, 11 figures

References in corpus (31)

• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Quantized Majorana conductance
• Milestones toward Majorana-based quantum computing
• Composite Majorana Fermion Wavefunctions in Nanowires
• SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum
• Exciting Andreev pairs in a superconducting atomic contact
• Direct microwave measurement of Andreev-bound-state dynamics in a proximitized semiconducting nanowire
• Spin-orbit splitting of Andreev states revealed by microwave spectroscopy
• Andreev quantum dots for spin manipulation
• Observation of the 4$\pi$-periodic Josephson effect in indium arsenide nanowires
• Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions
• Majorana splitting from critical currents in Josephson junctions
• Multiple Andreev reflection and critical current in topological superconducting nanowire junctions
• Phenomenology and Dynamics of Majorana Josephson Junction
• Signatures of topological Josephson junctions
• Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase
• Microwave signatures of Majorana states in a topological Josephson junction
• Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
• Signatures of topological phase transitions in Josephson current-phase discontinuities
• Josephson Current through a Semiconductor Nanowire: effect of strong spin-orbit coupling and Zeeman splitting
• Zeeman and spin-orbit effects in the Andreev spectra of nanowire junctions
• Probing a topological quantum critical point in semiconductor-superconductor heterostructures

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• Majorana nanowires for topological quantum computation
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• Topological Josephson Heat Engine
• Microwave spectroscopy of interacting Andreev spins
• Josephson Diode Effect in Topological Superconductor
• Thermodynamics in topological Josephson junctions
• Microwave Signatures of Topological Superconductivity in Planar Josephson Junctions
• Josephson current via an isolated Majorana zero mode
• Topological Josephson Bifurcation Amplifier: Semiclassical theory
• Quasiparticle poisoning in trivial and topological Josephson junctions
• Topological Josephson Junctions in the Integer Quantum Hall Regime
• Quantum-critical dynamics of a Josephson junction at the topological transition