Topological properties of Floquet winding bands in a photonic lattice

The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a two-coupled ring system we engineer an anomalous Floquet metal that is gapless in the bulk and shows simultaneously two different topological properties. On the one hand, this synthetic lattice presents bands characterised by a winding number. The winding emerges from the breakup of inversion symmetry and it directly relates to the appearance of Bloch suboscillations within its bulk. On the other hand, the Floquet nature of the lattice results in well-known anomalous insulating phases with topological edge states. The combination of broken inversion symmetry and periodic time modulation studied here enrich the variety of topological phases available in lattices subject to Floquet driving and suggest the possible emergence of novel phases when periodic modulation is combined with the breakup of spatial symmetries.