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

TL;DR

This paper proposes a new method to generate and manipulate Majorana bound states in planar Josephson junctions without external magnetic fields by coupling to skyrmion crystals, enabling topological quantum operations at higher temperatures.

Contribution

It introduces a novel approach using skyrmion crystals to achieve magnetic field-free Majorana bound states in planar Josephson junctions, facilitating their movement and braiding for quantum computing.

Findings

Skyrmion crystal coupling enables MBS without external magnetic fields.

Both s-wave and d-wave superconductors can generate MBS.

Higher temperature operation possible with d-wave superconductors.

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.