Magnetic field-free braiding and nontrivial fusion of Majorana bound states in high-temperature planar Josephson junctions

Abstract

Demonstration of non-Abelian statistics of Majorana bound states (MBS) is crucial for the realization of fault-tolerant topological quantum computation. Two-dimensional platforms such as planar Josephson junctions require an in-plane magnetic field to generate a pair of MBS at its non-superconducting channel ends; however, the fixed direction of the in-plane magnetic field puts a constraint on the realization of a multi-terminal topological planar junction, and hence its ability to physically move multiple MBS -- which is necessary for performing the fusion and braiding operations. Here we show that in a planar Josephson junction coupled to a skyrmion crystal, which can generate multiple pairs of MBS in the absence of any external magnetic field, the non-trivial fusion and braiding operations can be performed. Our numerical calculations, designed for realistic two-dimensional quantum systems, certify the feasibility of experimental realization of the proposed device schemes. We find that both $s$-wave and $d$-wave superconducting leads can generate the MBS; indicating that the MBS movement operations can be performed at higher temperatures using $d$-wave superconducting leads. Our results establish that the skyrmion crystal-coupled planar Josephson junction is a viable platform for the generation and controlled movement of the MBS.

9 pages, 5 figures

References in corpus (25)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Skyrmions in Magnetic Multilayers
• Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions
• Missing Shapiro steps in topologically trivial Josephson Junction on InAs quantum well
• Shadow epitaxy for in-situ growth of generic semiconductor/superconductor devices
• InSbAs two-dimensional electron gases as a platform for topological superconductivity
• Signatures of a topological phase transition in a planar Josephson junction
• Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions
• Skyrmion Control of Majorana States in Planar Josephson Junctions
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs
• On-demand large-conductance in trivial zero-bias tunneling peaks in Majorana nanowires
• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
• Floquet Majorana bound states in voltage-biased Planar Josephson Junctions
• Progress in superconductor-semiconductor topological Josephson junctions
• Magnetic properties of Co/Ni-based multilayers with Pd and Pt insertion layers
• Room-Temperature Magnetic Skyrmions in Pt/Co/Cu Multilayers
• Non-local transport signatures of topological superconductivity in a phase-biased planar Josephson junction
• 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
• Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions

Cited by in corpus (1)

• Diode effect in a skyrmion-coupled high-temperature Josephson junction