Braiding Floquet Majorana Modes in One-Dimensional Topological Superconductors

It is well-known that braiding Majorana zero modes in one-dimensional (1D) topological systems is a challenge since the modes hybridize when they are within proximity of each other. Recent developments have indicated that braiding in 1D can be accomplished through periodic driving. In our work, we study a 1D p-wave superconductor modelled as a Kitaev chain with the driving achieved by periodically modulating the parameters of the system. This Floquet system gives rise to Majorana edge modes of both zero and π quasienergy. We numerically implement the adiabatic protocol developed in Ref. [1] to braid the Floquet Majorana zero modes, using the Floquet Majorana π modes as an auxiliary degree of freedom. We consider the inclusion of interactions and disorder into the system and demonstrate the robustness of the protocol by examining quantities such as the exchange operator.

[1] B. Bauer et al., Phys. Rev. B 100, 041102 (2019).