Anomalous Floquet Phases. A resonance phenomena
arXiv:2312.06778 · doi:10.22331/q-2024-11-13-1522
Abstract
Floquet topological phases emerge when systems are periodically driven out-of-equilibrium. They gained attention due to their external control, which allows to simulate a wide variety of static systems by just tuning the external field in the high frequency regime. However, it was soon clear that their relevance goes beyond that, as for lower frequencies, anomalous phases without a static counterpart are present and the bulk-to-boundary correspondence can fail. In this work we discuss the important role of resonances in Floquet phases. For that, we present a method to find analytical solutions when the frequency of the drive matches the band gap, extending the well-known high frequency analysis of Floquet systems. With this formalism, we show that the topology of Floquet phases with resonances can be accurately captured in analytical terms. We also find a bulk-to-boundary correspondence between the number of edge states in finite systems and a set of topological invariants in different frames of reference, which crucially do not explicitly involve the micromotion. To illustrate our results, we periodically drive a SSH chain and a -flux lattice, showing that our findings remain valid in various two-band systems and in different dimensions. In addition, we notice that the competition between rotating and counter-rotating terms must be carefully treated when the undriven system is a semi-metal. To conclude, we discuss the implications to experimental setups, including the direct detection of anomalous topological phases and the measurement of their invariants.
20 pages, 12 figures and Appendix
References in corpus (63)
- Unpaired Majorana fermions in quantum wires
- Photonic Floquet Topological Insulators
- Classification of topological quantum matter with symmetries
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Photovoltaic Hall effect in graphene
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Observation of Floquet-Bloch states on the surface of a topological insulator
- Topological characterization of periodically-driven quantum systems
- Light-induced anomalous Hall effect in graphene
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
- Observation of topologically protected bound states in a one dimensional photonic system
- The Zak phase and the existence of edge states in graphene
- Floquet-Bloch theory and topology in periodically driven lattices
- Periodic Table for Floquet Topological Insulators
- 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
- Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
- Floquet Fractional Chern Insulator in Doped Graphene
- Multiterminal Conductance of a Floquet Topological Insulator
- Topological Origin of Equatorial Waves
- Merging of Dirac points and Floquet topological transitions in AC driven graphene
- Microscopic theory for the light-induced anomalous Hall effect in graphene
- Floquet topological transitions in a driven one-dimensional topological insulator
- Observation of anomalous π modes in photonic Floquet engineering
- Interplay between long range hopping and disorder in topological systems
- Periodically-driven quantum matter: the case of resonant modulations
- Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
- Higher-order Floquet topological phases with corner and bulk bound states
- Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
- Floquet engineering of long-range p-wave superconductivity
- Engineering Quantum Anomalous Hall Plateaus and Anti-Chiral States with AC Fields
- Dynamical synchronization transition in interacting electron systems
- Observation of pi/2 modes in an acoustic Floquet system
- Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift
- Wannier representation of Floquet topological states
- Anomalous and normal dislocation modes in Floquet topological insulators
- Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
- How to Directly Measure Floquet Topological Invariants in Optical Lattices
- Real-space detection and manipulation of topological edge modes with ultracold atoms
- Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
- Robustness of symmetry-protected topological states against time-periodic perturbations
- Simulation of 1D topological phases in driven quantum dot arrays
- Topological swing in Bloch oscillations
- Topological properties of Floquet winding bands in a photonic lattice
- Light-induced half-quantized Hall effect and axion insulator
- Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
- Light-induced phase crossovers in a quantum spin Hall system
- Dynamical construction of Quadrupolar and Octupolar topological superconductors
- Bridging the gap between topological non-Hermitian physics and open quantum systems
- Generation of higher-order topological insulators using periodic driving
- Charge-Density Wave Order on a -flux Square Lattice
- Charge localization and dynamical spin locking in double quantum dots driven by ac magnetic fields
- Flow Equations for Disordered Floquet Systems
- Transport signatures in topological systems coupled to AC fields
- Topological modes in stellar oscillations
- Floquet engineering of Dirac cones on the surface of a topological insulator
- Multi-qudit interactions in molecular spins
- Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks
- Designing adiabatic time-evolution from high frequency bichromatic sources
- Transport blocking and topological phases using ac magnetic fields