Dynamical Symmetry Indicators for Floquet Crystals

Abstract

Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the "inherently dynamical" Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.

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References in corpus (93)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Photovoltaic Hall effect in graphene
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• The (High Quality) Topological Materials In The World
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Floquet Engineering of Quantum Materials
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Catalogue of Topological Electronic Materials
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Inversion Symmetric Topological Insulators
• Observation of photonic anomalous Floquet Topological Insulators
• Topology of crystalline insulators and superconductors
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Wannier representation of Z_2 topological insulators
• High-throughput calculations of magnetic topological materials
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Fragile Topology and Wannier Obstructions
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Periodic Table for Floquet Topological Insulators
• Realization of an anomalous Floquet topological system with ultracold atoms
• Topological singularities and the general classification of Floquet-Bloch systems
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Floquet generation of Majorana end modes and topological invariants
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Classification of topological phases in periodically driven interacting systems
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Optically engineering the topological properties of a spin Hall insulator
• Measuring topology by dynamics: Chern number from linking number
• An anomalous higher-order topological insulator
• Surfaces of Axion Insulators
• Topological non-symmorphic crystalline insulators
• Rotation Anomaly and Topological Crystalline Insulators
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Topology of Disconnected Elementary Band Representations
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Floquet symmetry-protected topological phases in cold atomic systems
• Higher-order Floquet topological phases with corner and bulk bound states
• Coupled-wire construction of static and Floquet second-order topological insulators
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Floquet topological phases protected by time glide symmetry
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• Complex classes of periodically driven topological lattice systems
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Measurement-only quantum computation with Majorana corner modes
• Space-time crystal and space-time group
• Floquet generation of Second Order Topological Superconductor
• Higher Order Topological Insulator via Periodic Driving
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• Symmetry indicators of band topology
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Topological magnetic crystalline insulators and co-representation theory
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Wannier representation of Floquet topological states
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Floquet edge states in a harmonically driven integer quantum Hall system
• Time-induced second-order topological superconductors
• Tunable Fragile Topology in Floquet Systems
• Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure
• Symmetry Analysis of Anomalous Floquet Topological Phases
• Superconductors with anomalous Floquet higher-order topology
• Floquet Majorana bound states in voltage-biased Planar Josephson Junctions
• Anomalous Floquet topological crystalline insulators
• Dynamical Fragile Topology in Floquet Crystals
• Anatomy of a periodically driven p-wave superconductor
• Intertwined Space-Time Symmetry, Orbital Magnetism and Dynamical Berry Curvature in a Circularly Shaken Optical Lattice