Suppression of odd-frequency pairing by phase-disorder in a nanowire coupled to Majorana zero modes

Abstract

Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We here point out that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase-disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged $T$-matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e. superconducting, part of the $T$-matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk 1D odd-$\omega$ superconductivity from MZMs demand full control of the system parameters.

arXiv comment15 pages, 7 figures

References in corpus (41)

• Non-Abelian Anyons and Topological Quantum Computation
• 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
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Majorana fermions in a tunable semiconductor device
• Majorana Zero Modes and Topological Quantum Computation
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Majorana Fermion Induced Resonant Andreev Reflection
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Long-range effects in superconductor-ferromagnet structures
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Transport spectroscopy of NS nanowire junctions with Majorana fermions
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Gate-tuned normal and superconducting transport at the surface of a topological insulator
• Quantum Spin Fluctuations as a Source of Long-Range Proximity Effects in Diffusive Ferromagnet-Superconductor Structures
• Odd-frequency superconductivity
• Composite Majorana Fermion Wavefunctions in Nanowires
• Next steps of quantum transport in Majorana nanowire devices
• Colloquium: Atomic spin chains on surfaces
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Intrinsic Paramagnetic Meissner Effect due to s-wave Odd-Frequency Superconductivity
• Odd-frequency superconducting pairing in one-dimensional systems
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Spin-dependent coupling between quantum dots and topological quantum wires
• Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling
• Conductance signatures of odd-frequency superconductivity in quantum spin Hall systems using a quantum point contact
• The Majorana STM as a perfect detector of odd-frequency superconductivity
• Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• Odd frequency pairing of interacting Majorana fermions
• Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point
• Odd-frequency superconducting pairing in Kitaev-based junctions

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• Phase-tunable electron transport assisted by odd-frequency Cooper pairs in topological Josephson junctions
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• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Emergent pair symmetries in systems with poor man's Majorana modes
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• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
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• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states
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