Network Models of Photonic Floquet Topological Insulators

Abstract

A recently-proposed class of photonic topological insulators is shown to map onto Chalker-Coddington-type networks, which were originally formulated to study disordered quantum Hall systems. Such network models are equivalent to the Floquet states of periodically-driven lattices. We show that they can exhibit topologically protected edge states even if all bands have zero Chern number, which is a characteristic property of Floquet bandstructures. These edge states can be counted by an adiabatic pumping invariant based on the winding number of the coefficient of reflection from one edge of the network.

References in corpus (14)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Photovoltaic Hall effect in graphene
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological characterization of periodically-driven quantum systems
• Exploring Topological Phases With Quantum Walks
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions

Cited by in corpus (67)

• Topological Photonics
• Floquet Topological Insulators for Sound
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Topological acoustics
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Topological photonic crystals: physics, designs and applications
• Topological index for periodically driven time-reversal invariant 2D systems
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Measurement of a topological edge invariant in a microwave network
• A perspective on topological nanophotonics: current status and future challenges
• Optical isolation with nonlinear topological photonics
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices
• Exceptional Points in a Non-Hermitian Topological Pump
• Hybrid skin-topological modes without asymmetric couplings
• Topological Effects in Chiral Symmetric Driven Systems
• Topological metasurface: From passive toward active and beyond
• Realization of Anomalous Floquet Insulators in Strongly-Coupled Nanophotonic Lattices
• Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice
• Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators
• Dynamically manipulating topological physics and edge modes in a single degenerate optical cavity
• Topological phases in ring resonators: recent progress and future prospects
• Observation of topological edge states of sound at a momentum away from the high-symmetry point
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• Photonic ${\mathbb{Z}}_2$ topological Anderson insulators
• PT Symmetric Floquet Topological Phase
• Floquet Weyl Phases in a Three Dimensional Network Model
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Phase rotation symmetry and the topology of oriented scattering networks
• Phase spectroscopy of topological invariants in photonic crystals
• Topological Invariants in Point Group Symmetric Photonic Topological Insulators
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Reconfigurable Microwave Photonic Topological Insulator
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
• Topological swing in Bloch oscillations
• Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene
• Non-diffracting states in one-dimensional Floquet photonic topological insulators
• Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
• Topological Floquet edge states in periodically curved waveguides
• Engineering topological edge states in two dimensional magnetic photonic crystal
• Topological Phenomena in Classical Optical Networks
• Topological edge states in two-gap unitary systems: A transfer matrix approach
• Topological boundary invariants for Floquet systems and quantum walks
• Topological chiral modes in random scattering networks
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Network model for periodically strained graphene
• Quantum Hall network models as Floquet topological insulators
• Dynamical Detection of Topological Spectral Density
• Topological Sensing with Photonic Arrays of Resonant Circular Waveguides
• Network model for higher-order topological phases
• Effective Floquet model for minimally twisted bilayer graphene
• Topological phases of an interacting Majorana Benalcazar-Bernevig-Hughes model
• Tachyonic Dispersion in Coherent Networks
• Topological Flat Band and Parity-Time Symmetry in a Honeycomb Lattice of Coupled Resonant Optical Waveguides
• Topological chiral interface states beyond insulators
• Topological edge states in photonic Floquet insulator with unpaired Dirac cones
• Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice
• Floquet Topological Dissipative Kerr Solitons and Incommensurate Frequency Combs
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Magnetless Circulators Based on Synthetic Angular-Momentum Bias: Recent Advances and Applications
• N-Band Photonic Hopf Insulators Based on 2D Microring Lattices
• Signature of edge states in resonant wave scattering
• Experimental demonstration of an anomalous Floquet topological insulator based on negative-index media
• Chiral electronic network within skyrmionic lattice on topological insulator surfaces
• Tunable Topological Phases in Quantum Kirigamis
• Anomalous nonreciprocal topological networks: stronger than Chern insulators
• Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice