Layer Construction of Floquet Topological Phases*

Periodically driven systems can exhibit anomalous transport at the boundary of an open system, even when the bulk (quasienergy) bands are topologically trivial. We introduce a layer construction for Floquet phases without symmetry that is applicable to any even spatial dimension. This allows topologically nontrivial phases to be constructed from class AIII Hamiltonians in one lower dimension. This construction has the advantage that along one dimension it requires only nearest-neighbour interactions, making the resulting models particularly suitable for experimental realisations involving synthetic dimensions. We motivate the layer construction in the context of free fermions, and go on to discuss its applicability to interacting systems.