Floquet and anomalous Floquet Weyl semimetals

The periodic driving of a quantum system can enable new topological phases without analogs in static systems. This provides a route towards preparing nonequilibrium quantum phases rooted in the nonequilibrium nature by periodic driving engineering. Motivated by the ongoing considerable interest in topological semimetals, we are interested in the novel topological phases in the periodically driven topological semimetals without a static counterpart. We propose to design nonequilibrium topological semimetals in the regime of a weakly driving field where the spectrum width has the same magnitude as the driving frequency. We identify two types of nonequilibrium Weyl semimetals (i.e., Floquet and anomalous Floquet Weyl semimetals) that do not exhibit analogs in equilibrium. The proposed setup is shown to be experimentally feasible using the state-of-the-art techniques used to control ultracold atoms in optical lattices.