Square-root Floquet topological phases and time crystals

Periodically driven (Floquet) phases are attractive due to their ability host unique physical phenomena with no static counterparts. We propose a general approach in nontrivially devising square-root version of existing Floquet phases, applicable both noninteracting and interacting setting. The resulting systems found yield richer physics that is otherwise absent the original counterparts robust against parameter imperfection. These include emergence topological superconductors arbitrarily many zero, $\pi$, $\pi/2$ edge modes, as well $4T$-period time crystals disordered disorder-free ($T$ being driving period). Remarkably, our can be repeated indefinitely obtain 2nth-root given system, thus allowing for discovery systematic construction family exotic phases.