Time-Crystalline Topological Superconductors*

Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce the notion of 1D time-crystalline topological superconductors, for which time-translation symmetry breaking and Majorana physics nontrivially intertwine. In the simplest realization, such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with unconventional Floquet Majorana end modes that recover their initial form only after four drive periods. We also propose experimental implementations and detection schemes for this new phase.