Driven Majorana Fermions: A Route to Synthetic p_x+ip_y Superconductors

We propose a protocol to realize mobile Majorana zero modes (MZMs) and effective p_x + ip_y superconductors in the Kitaev model. By introducing a spatially modulated chemical potential, MZMs are stabilized at the boundaries between domains of normal and topological superconducting phases. Moreover, as the modulated chemical potential pattern varies with time, the MZMs travel with the moving domain walls. This time-dependent pattern can be viewed as a Majorana pump, which moves the localized zero modes from one end of the system to the other end. Importantly, analogous to the scenario of a Chern insulator induced by a Thouless pump, we show that the Majorana pump could lead to a p_x +ip_y superconductor in the two-dimensional space of space and synthetic time. We analyze the periodic pumping of MZMs using the Floquet theory and demonstrate how the p_y pairing emerges even when there is only the p_x pairing in the original model. Finally, experimental realizations of the physics will be discussed.