Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions

Abstract

Planar Josephson junctions are theoretically predicted to harbor zero-energy Majorana bound states (MBS) in a tunable two-dimensional geometry, at the two ends of the middle metallic channel. Here we show that three distinct topological superconducting regimes, governing the localization of the near-zero-energy MBS, appear in these planar Josephson junctions. The topologically-protected MBS appear near the narrow edges of the junction -- not only in the middle metallic channel but also in the superconducting leads which have widths similar to the values used in recent experiments. We incorporate random fluctuation in the chemical potential to investigate the influence of non-magnetic disorder on the localization of the MBS in different topological regimes and find that the MBS are quite robust against disorder because of the two-dimensional geometry. Interestingly, moderate amount of disorder reduces the splitting between the MBS pairs, possibly by minimizing the wave function overlap of the MBS. We also discuss the changes in the topological superconducting phases when the superconducting lead width is varied. Our results reveal a rich structure of the localization of topologically protected multiple MBS in experimentally-accessible planar Josephson junctions, and call for their experimental confirmation.

17 pages, 14 figures

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Majorana Fermions in Chiral Topological Ferromagnetic Nanowires
• Tunable magnetic textures in spin valves: From spintronics to Majorana bound states
• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Tunable planar Josephson junctions driven by time-dependent spin-orbit coupling
• Non-local transport signatures of topological superconductivity in a phase-biased planar Josephson junction
• Microwave Signatures of Topological Superconductivity in Planar Josephson Junctions
• Design of a Majorana trijunction
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Majorana bound states in d-wave superconductor planar Josephson junction
• Challenges in detecting topological superconducting transitions via supercurrent and phase probes in planar Josephson junctions
• Majorana bound state parity exchanges in planar Josephson junctions

Cited by in corpus (2)

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