From fractional solitons to Majorana fermions in a paradigmatic model of topological superconductivity

Abstract

Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gapped phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.

5 pages, 2 figures

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• Fractional Fermions with Non-Abelian Statistics
• Manipulation with Andreev states in spin active mesoscopic Josephson junctions
• The chiral anomaly in real space

Cited by in corpus (24)

• Theory of Majorana zero modes in unconventional superconductors
• Majorana bound states in semiconducting nanostructures
• Floquet engineering bulk odd-frequency superconducting pairs
• Formation and detection of Majorana modes in quantum spin Hall trenches
• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions
• Emerging topological bound states in Haldane model zigzag nanoribbons
• Topological Solitons in Su-Schrieffer-Heeger Chain with periodic hopping modulation, domain walls and disorder
• Signatures of Jackiw-Rebbi resonance in the thermal conductance of topological Josephson junctions with magnetic islands
• Topological isoconductance signatures in Majorana nanowires
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Exciting odd frequency equal-spin-triplet correlations at metal-superconductor interfaces
• Reconstruction-Induced ${\phi }_0$ Josephson Effect in Quantum Spin Hall Constrictions
• Charging a Dimerized Quantum XY Chain
• Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping
• Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
• Confinement-induced zero-bias peaks in conventional superconductor hybrids
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• Few-body precursors of topological frustration
• Anomalous flux periodicity in proximitised quantum spin Hall constrictions
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Spin responses of a disordered helical superconducting edge under Zeeman field