Spacetime symmetry indicator for Floquet topological states

Symmetry plays an important role in topological states. In a band insulator, usually the band topology is a global property of Bloch wavfunctions over the whole Brillouin zone. In the presence of crystalline symmetries, however, the band topology can sometimes be inferred just from knowledge of Bloch wavefunctions at high symmetry momenta in k space, known as symmetry indicators. In this work, we generalize the concept of symmetry indicators from spatial crystalline symmetries to spacetime symmetry in periodically driven Floquet systems. In the presence of spacetime screw symmetry, a combination of time translation and spatial rotation, we derive the symmetry indicators for Floquet topological insulators in 2+1-D. This provides a convenient tool to identify and engineer nontrivial Floquet topological phases in periodically driven materials.