Floquet quadrupole photonic crystals protected by space-time symmetry

Quadrupole topological insulators with nontrivial and quantized second-order moments, which can protect zero-dimensional corner states two dimensions lower than the bulk, are potentially useful in optoelectronic applications. So far, such quadrupole phases are studied in lattice models with synthetic symmetries or patterned dielectric medium with spatial symmetries. In this work, we present a Floquet quadrupole topological insulator in a nonlinear photonic crystal. The nontrivial quadrupole phase is protected and quantized by a space-time screw symmetry. This symmetry is induced by both the nonlinear susceptibilities of the material and the external driving field. We confirm the quantized second-order moment by both symmetry indices analysis and numerical calculations of the nested-Wilson loop. Key features including fractional occupation and filling anomalies are observed.