Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators

Abstract

In this work, we reported a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and realization of spontaneous discrete time-translation symmetry (DTS) breaking in our model require necessarily coexistence of anomalous topological invariants (0 modes and $\pi$ modes), instead of the presence of disorders or many-body localization. We found that in a particular frequency range of the underlying drive, the anomalous Floquet phase coexistence between zero and pi modes can produce the period-doubling (2T, two cycles of the drive) that breaks the spontaneously, leading to the subharmonic response ($\omega /2$, half the drive frequency). The rigid period-oscillation is topologically-protected against perturbations due to both non-trivially opening of 0 and $\pi$-gaps in the quasienergy spectrum, thus, as a result, can be viewed as a specific "Rabi oscillation" between two Floquet eigenstates with certain quasienergy splitting $\pi /T$. Our modeling of the time-crystalline 'ground state' can be easily realized in experimental platforms such as topological photonics and ultracold fields. Also, our work can bring significant interests to explore topological phase transition in Floquet systems and to bridge the gap between Floquet topological insulators and photonics, and period-doubled time crystals.

arXiv comment31 pages, 6 figures, 2 supplementary figures

References in corpus (61)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Observation of a Discrete Time Crystal
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• Topological phases of fermions in one dimension
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Discrete time crystals: rigidity, criticality, and realizations
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Observation of the topological soliton state in the Su-Schrieffer-Heeger model
• Absence of Quantum Time Crystals
• Localization protected quantum order
• Classical Time Crystals
• Modeling spontaneous breaking of time-translation symmetry
• Discrete Time Crystals
• Boundary time crystals
• Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Pre-thermal phases of matter protected by time-translation symmetry
• Classification of topological phases in periodically driven interacting systems
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Observation of time quasicrystal and its transition to superfluid time crystal
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Observation of a space-time crystal in a superfluid quantum gas
• Floquet topological transitions in a driven one-dimensional topological insulator
• Temporal order in periodically driven spins in star-shaped clusters
• Observation of anomalous π modes in photonic Floquet engineering
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
• Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Simulation of non-Abelian braiding in Majorana time crystals
• Floquet time crystals in clock models
• Complex classes of periodically driven topological lattice systems
• Floquet engineering of long-range p-wave superconductivity
• Superfluidity and Space-Time Translation Symmetry Breaking
• Time crystals in periodically driven systems
• Period-$n$ discrete time crystals and quasicrystals with ultracold bosons
• Time crystal platform: from quasi-crystal structures in time to systems with exotic interactions
• Time crystals: analysis of experimental conditions
• Defining Time Crystals via Representation Theory
• Floquet analysis of a quantum system with modulated periodic driving
• Time crystal behavior of excited eigenstates
• Topological Time Crystals
• Spin and topological order in a periodically driven spin chain
• Discrete time crystals in many-body quantum chaos
• Realizing time crystals in discrete quantum few-body systems
• Time-crystalline Topological Superconductors
• Floquet Supersymmetry

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• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Topological properties of a periodically driven Creutz ladder
• Topologically protected boundary discrete time crystal for a solvable model
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Time crystal embodies chimeralike state in periodically driven quantum spin system
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits