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High-order topological phases, such as those with nontrivial quadrupole moments, protect edge states that are themselves topological insulators in lower dimensions. So far, most quadrupole phases of light are explored in linear optical systems, which are protected by spatial symmetries or synthetic symmetries. Here we present Floquet quadrupole phases in driven nonlinear photonic crystals (PhCs) that are protected by space-time screw symmetries. We start by illustrating space-time symmetries by tracking the trajectory of instantaneous optical axes of the driven media. Our Floquet quadrupole phase is then confirmed in two independent ways: symmetry indices at high-symmetry momentum points and calculations of the nested Wannier bands. Our work presents a general framework to analyze symmetries in driven optical materials and paves the way to further exploring symmetry-protected topological phases in Floquet systems and their optoelectronic applications.
We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coheren
Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theorie
This letter is devoted to point out a specific character of the Finite-Difference-Time-Domain method through the study of nano-structures supporting geometrical symmetry-protected modes that can not be excited at certain conditions of illumination. T
Chiral spin textures are researched widely in condensed matter systems and show potential for spintronics and storage applications. Along with extensive condensed-matter studies of chiral spin textures, photonic counterparts of these textures have be
We show that homogeneous lattice gauge theories can realize nonequilibrium quantum phases with long-range spatiotemporal order protected by gauge invariance instead of disorder. We study a kicked $mathbb{Z}_2$-Higgs gauge theory and find that it brea