Abstract

Majorana zero-modes in a superconductor are midgap states localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics. This statistics can also be expressed in terms of a non-deterministic fusion rule: when two vortices merge they may or they may not produce an unpaired fermion with equal probability. When the vortices are immobile, one cannot demonstrate their statistics by exchanging them in real space and indirect methods are needed. As a real-space alternative, we propose two protocols which use the chiral motion along the boundary of the superconductor. The first protocol allows one to braid a mobile vortex in the edge channel with an immobile vortex in the bulk. The edge vortices (π-phase domain walls) are created on demand by a voltage pulse at a Josephson junction. The braiding with a Majorana zero-mode in the bulk is detected by the charge which is deterministically produced upon their fusion. The second protocol demonstrates the non-deterministic fusion rule of such mobile vortices, which manifests itself in a nonlocally correlated charge transfer.