Topologically protected braiding in a single wire using Floquet Majorana modes*

The non-Abelian nature of Majorana zero modes is most prominently exhibited through braiding. While originally formulated for 2D systems, it has been shown that braiding can also be realized using 1D wires by forming an essentially 2D network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and Pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes non-local braiding of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the Pi modes as auxiliary degrees of freedom.