Dynamical simulation of the injection of vortices into a Majorana edge mode

TL;DR

This paper presents a time-dependent simulation of vortex injection into Majorana edge modes, revealing dynamics beyond adiabatic approximations and informing topological qubit implementation.

Contribution

It introduces a dynamic many-body simulation of vortex injection and braiding in topological superconductors, surpassing previous static models.

Findings

Demonstrates vortex injection dynamics beyond adiabatic approximation

Shows how junction properties affect vortex braiding success

Provides insights for implementing topological qubits

Abstract

The chiral edge modes of a topological superconductor can transport fermionic quasiparticles, with Abelian exchange statistics, but they can also transport non-Abelian anyons: Edge-vortices bound to a $\pi$-phase domain wall that propagates along the boundary. A pair of such edge-vortices is injected by the application of an $h/2e$ flux bias over a Josephson junction. Existing descriptions of the injection process rely on the instantaneous scattering approximation of the adiabatic regime [Beenakker et al. Phys.Rev.Lett. 122, (2019)], where the internal dynamics of the Josephson junction is ignored. Here we go beyond that approximation in a time-dependent many-body simulation of the injection process, followed by a braiding of mobile edge-vortices with a pair of immobile Abrikosov vortices in the bulk of the superconductor. Our simulation sheds light on the properties of the Josephson junction needed for a successful implementation of a flying topological qubit.