Multi-topological Floquet metals in a photonic lattice

Topological materials are usually classified according to a single topological invariant. The engineering of synthetic structures characterised by more than one class of topological invariants would open the way to the combination of different topological properties, enlarging the richness of topological phase diagrams. 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 that directly relates to the period of Bloch oscillations within its bulk. On the other, the Floquet nature of our implementation results in well-known anomalous insulating phases with topological edge states. Our experiments open the way to study unconventional multi-topological phases in synthetic lattices.