Photonic analogues of the Haldane and Kane-Mele models

Abstract

The condensed matter Haldane and Kane-Mele models revolutionized the understanding of what is an "insulator", as they unveiled novel classes of media that behave as metals near the surface, but are insulating in the bulk. Here, we propose exact electromagnetic analogues of these two influential models relying on a photonic crystal implementation of "artificial graphene" subject to an effective magnetic field. For the Haldane model, the required effective magnetic field for photons can be emulated with a spatially variable pseudo-Tellegen response. For the Kane-Mele model, the spin-orbit coupling can be mimicked using matched anisotropic dielectrics with identical permittivity and permeability, without requiring any form of bianisotropic couplings. Using full wave numerical simulations and duality theory we verify that the nontrivial topology of the two proposed platforms results in the emergence of topologically protected gapless edge states at the interface with a trivial photonic insulator. Our theory paves the way for the emulation of the two condensed matter models in a photonic platform, and determines another paradigm to observe topologically protected edges-states in a fully reciprocal all-dielectric and non-uniform anisotropic metamaterial.

arXiv comment4 figures, 2 animations

References in corpus (32)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Analogs of quantum Hall effect edge states in photonic crystals
• A topological quantum optics interface
• Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons
• Artificial graphene as a tunable Dirac material
• Observation of novel edge states in photonic graphene
• Three-Dimensional All-Dielectric Photonic Topological Insulator
• Extremal transmission at the Dirac point of a photonic band structure
• Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --
• Engineering artificial graphene in a two-dimensional electron gas
• Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene
• Scattering-Free Optical Edge States between Heterogeneous Photonic Topological Insulators
• Gauge Field Optics with Anisotropic Media
• Dirac Spectra and Edge States in Honeycomb Plasmonic Lattices
• PTD Symmetry Protected Scattering Anomaly in Optics
• Enabling single-mode behavior over large areas with photonic Dirac cones
• Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Realizing Haldane Model in Fe-based Honeycomb Ferromagnetic Insulators
• Exact Solution for the Protected TEM edge mode in a PTD-Symmetric Parallel-Plate Waveguide
• Topological origin of electromagnetic energy sinks
• Quantized Angular Momentum in Topological Optical Systems
• Link between the photonic and electronic topological phases in artificial graphene
• Effective Hamiltonian for electron waves in artificial graphene: A first principles derivation

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• Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model
• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Photonic band structure design using persistent homology
• Topological Phases in Fractals: Local Spin Chern Marker in the Sierpinski carpet Kane-Mele-Rashba Model
• Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling
• Haldane graphene billiards versus relativistic neutrino billiards
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• Classification of Topological Phase in 2D Photonic Continuous Media Using Electromagnetic Parameters