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

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: Majorana zero-modes bound to a {\pi}-phase domain wall that propagates along the boundary. Such an edge vortex 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, 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 the mobile edge vortex with an immobile Abrikosov vortex 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 Majorana qubit.Comment: 13 pages 12 figure