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 (7)

• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• 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
• Plasmonic edge states: an electrostatic eigenmode description
• Far-infrared Tamm polaritons in a microcavity with incorporated graphene sheet

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