Spacetime symmetry indicators for two-dimensional Floquet topological insulators

Floquet Topological Insulators (FTIs) in two spatial dimensions can exhibit anomalous chiral edge modes despite a fully localized bulk, captured by a new topological invariant other than the Chern number. In this work, we focus on $(2+1)D$ FTIs in symmetry class A with a spacetime symmetry known as $n$-fold time screw symmetry. We show that the bulk invariant can be partially determined by symmetry indicators associated with $n=2,3,4,6$ time screw symmetry, which only depend on the time evolution in high symmetry momenta. We derive a simple formula that relates symmetry indicators to the bulk invariant, and demonstrates its validity in examples of FTI models. Our results can simplify the engineering of FTIs in real materials, and especially shed light on systems driven by circularly polarized light.