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: 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.

13 pages 13 figures

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure
• Tkwant: a software package for time-dependent quantum transport
• Half-integer charge injection by a Josephson junction without excess noise
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Braiding Majorana Zero Mode in An Electrically Controllable Way

Cited by in corpus (1)

• Non-Abelian anyon statistics through AC conductance of a Majorana interferometer