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We propose a protocol to realize synthetic $p_x+ip_y$ superconductors inone-dimensional topological systems that host Majorana fermions. Byperiodically driving a localized Majorana mode across the system, our protocolrealizes a topological pumping of Majorana fermions, analogous to the adiabaticThouless pumping of electrical charges. Importantly, similar to the realizationof a Chern insulator through Thouless pumping, we show that pumping of Majoranazero modes could lead to a $p_x + ip_y$ superconductor in the two dimensions ofspace and synthetic time. The Floquet theory is employed to map the drivenone-dimensional system to a two-dimensional synthetic system by consideringfrequency as a new dimension. We demonstrate such Floquet $p_x + i p_y$superconductors using the Kitaev $p$-wave superconductor chain, a prototypical1D topological system, as well as its more realistic realization in the 1DKondo lattice model as examples. We further show the appearance of a new $\pi$Majorana mode at the Floquet zone boundary in an intermediate drive frequencyregion. Our work suggests a driven magnetic spiral coupled to a superconductoras a promising platform for the realization of novel topologicalsuperconductors.

Driven Majorana Modes: A Route to Synthetic $p_x+ip_y$ Superconductivity