Braiding Majorana Fermions with Magnetic Skyrmions

After a decade of intense theoretical and experimental efforts, demonstrating braiding of Majorana fermions remains an unsolved problem in condensed matter physics due to platform specific challenges. In this work, we propose topological superconductor (tSC) – magnetic multilayer (MML) heterostructures, with on-chip microwave cavity readout, as a novel platform for initializing, braiding, and reading out Majorana fermions. Stray fields from a skyrmion (Sk) in the MML can nucleate a vortex (Vx) in the tSC, known to host Majorana bound states (MBS) at its core. We show that our nucleation and braiding scheme can be achieved with a variety of existing options for tSC and MML. We further demonstrate that the Sk and the Vx bind strongly and move together without dissociation up to speeds enough to complete Majorana braiding within quasiparticle poisoning time. By patterning the MML into a track and by driving Sks in the MML with local spin-orbit torques, we show that the Sk-Vx compound objects can be efficiently moved along the track, thereby facilitating braiding of the Majorana modes at the centers of the Vxs. Finally, we show that the coupling of the MBS to the cavity field leads to easily observable parity dependent dispersive shift of the resonator frequency.