Floquet quadrupole photonic crystals protected by space-time symmetry

Abstract

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.

References in corpus (35)

• Quantum Spin Hall Effect in Graphene
• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Experimental realisation of the topological Haldane model
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Topolectrical circuit realization of topological corner modes
• Observation of a phononic quadrupole topological insulator
• Floquet Engineering of Quantum Materials
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Photonic quadrupole topological phases
• Observation of second-order topological insulators in sonic crystals
• Experimental Observation of Large Chern numbers in Photonic Crystals
• Experimental discovery of bulk-disclination correspondence
• Magnetic Topological Quantum Chemistry
• A fractional corner anomaly reveals higher-order topology
• Floquet Topological States in Shaking Optical Lattices
• Quadrupole Topological Photonic Crystals
• Higher-order topological insulators in synthetic dimensions
• Symmetry-protected hierarchy of anomalous multipole topological band gaps in nonsymmorphic metacrystals
• Floquet Chern Insulators of Light
• Space-time crystal and space-time group
• Anomalous quantum Hall effect of light in Bloch-wave modulated photonic crystals

Cited by in corpus (5)

• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Dynamical Detection of Topological Spectral Density
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Gapless higher-order topology and corner states in Floquet systems