Topological Photonic Tamm-States and the Su-Schrieffer-Heeger Model

Abstract

In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed.

13 pages

References in corpus (37)

• Topological Photonics
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Topological Boundary Modes in Isostatic Lattices
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Topological States on the Gold Surface
• Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
• The Zak phase and the existence of edge states in graphene
• Observation of the topological Anderson insulator in disordered atomic wires
• Topological phases of generalized Su-Schrieffer-Heeger models
• Unconventional quantum optics in topological waveguide QED
• Topological photonic crystal nanocavity laser
• Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• The effects of retardation on the topological plasmonic chain: plasmonic edge states beyond the quasistatic limit
• Fluctuations and noise-limited sensing near the exceptional point of $\mathcal{P}\mathcal{T}$-symmetric resonator systems
• Measurement of the Zak phase of photonic bands through the interface states of metasurface/photonic crystal
• A perspective on topological nanophotonics: current status and future challenges
• Topological collective plasmons in bipartite chains of metallic nanoparticles
• Geometrical Aspects in Optical Wavepacket Dynamics
• Su-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States
• Spectral imaging of topological edge states in plasmonic waveguide arrays
• Bulk-edge correspondence and long range hopping in the topological plasmonic chain
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Experimental demonstration of the robust end state in a split-ring-resonator chain
• Evidence of Excitonic Optical Tamm States using Molecular Materials
• Effect of photonic spin-orbit coupling on the topological edge modes of a Su-Schrieffer-Heeger chain
• Finite size effects on topological interface states in one-dimensional scattering systems
• Nonreciprocal resonant transmission/reflection based on a one-dimensional photonic crystal adjacent to the magneto-optical metal film
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Controlling Interface States in 1D Photonic Crystals by tuning Bulk Geometric Phases
• Modal expansions in periodic photonic systems with material loss and dispersion
• Plasmonic edge states: an electrostatic eigenmode description
• Localized Plasmons in Topological Insulators
• Far-infrared Tamm polaritons in a microcavity with incorporated graphene sheet
• A Bipartite Kronig-Penney Model with Dirac Potential Scatterers

Cited by in corpus (15)

• A brief review of topological photonics in one, two, and three dimensions
• Tamm plasmon polariton in planar structures: A brief overview and applications
• Short-Pulsed Metamaterials
• Nonlocal effects in temporal metamaterials
• Topological Graphene plasmons in a plasmonic realization of the Su-Schrieffer-Heeger Model
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Polaritonic Tamm states induced by cavity photons
• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
• Inner non-Hermitian skin effect on Bethe lattice
• Topology in a one-dimensional plasmonic crystal
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Loss-driven gain enhancements driven by topological singularities in non-Hermitian photonic crystals defects
• Internal wave crystals
• Topological optical and phononic interface mode by simultaneous band inversion