$q$th-root non-Hermitian Floquet topological insulators

Abstract

Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $\pm (0,1,...2^n)\pi /2^n$ and $\pm (0,1,...,3^n)\pi /3^n$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

arXiv commentAccepted version

References in corpus (72)

• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Atomic quantum gases in periodically driven optical lattices
• Non-Bloch Band Theory of Non-Hermitian Systems
• Floquet Engineering of Quantum Materials
• Light-induced anomalous Hall effect in graphene
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Observation of topologically protected bound states in a one dimensional photonic system
• Floquet topological insulators
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Non-Hermitian Topological Invariants in Real Space
• Periodic Table for Floquet Topological Insulators
• New topological invariants in non-Hermitian systems
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Realization of an anomalous Floquet topological system with ultracold atoms
• Topological singularities and the general classification of Floquet-Bloch systems
• Topological states of non-Hermitian systems
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Topology and Broken Symmetry in Floquet Systems
• Observation of non-Bloch parity-time symmetry and exceptional points
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Measuring quantized circular dichroism in ultracold topological matter
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Measurement of a topological edge invariant in a microwave network
• Topological tight-binding models from non-trivial square roots
• Floquet Topological Phases of Non-Hermitian Systems
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Realization of the square-root higher-order topological insulator in electric circuits
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Simulation of non-Abelian braiding in Majorana time crystals
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Acoustic square-root topological insulators
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Measurement-only quantum computation with Majorana corner modes
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Quantized classical response from spectral winding topology
• Quantum computation via Floquet topological edge modes
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Dynamical characterization of non-Hermitian Floquet topological phases in one-dimension
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• One-dimensional $2^n$-root topological insulators and superconductors
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Dual topological characterization of non-Hermitian Floquet phases
• Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain
• Systematic construction of square-root topological insulators and superconductors
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Dynamic winding number for exploring band topology
• Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model
• Square-root topological semimetals
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• PT Symmetric Floquet Topological Phase in SSH Model
• Square-root topological phase with time-reversal and particle-hole symmetry
• Matryoshka approach to Sine-Cosine topological models
• Photonic Floquet time crystals
• Controlling Exceptional Points with Light
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
• Light-driven Lifshitz transitions in non-Hermitian multi-Weyl semimetals
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Hexagonally warped exceptional physics in multi-Weyl semimetals
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder