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. arXiv:2001.10628v1 [cond-mat.mes-hall]

Edge states of Floquet-Dirac semimetal in a laser-driven semiconductor quantum-well

“…This work shows that the nearly resonant laser-excitation gives rise to the fourfold accidental degeneracies at the high-symmetry points, and the resulting Floquet DSM states host un- Moreover, the studies on the interrelation between a Tamm state and a topological edge state have been rapidly noticed, because the state-of-the-art techniques of fabrication of optical waveguide arrays and photonic crystals have made it possible to create both edge states by mimicking the one-dimensional Su-Schriefer-Hegger model [39][40][41][42]45,52,53 and more compli-cated systems. 43,44,46 In this work, both of the edge states are transformed in a continuous manner as a function of the single parameter F x without changing the composition and structure of the system, which draws a sharp distinction from these existing studies.…”

“…34 As regards edge states of the Floquet DSM states, Tamm states 35-37 appearing in the surfaces of several Dirac materials are theoretically examined. 38 Recently, growing interest has been captured in the interrelation of Tamm states with topological edge states in optical waveguide arrays, [39][40][41][42] 1D photonic crystals, [43][44][45] a graphene ring with the Aharonov-Bohm effect, 46 a honeycomb magnon insulator, 47 and a gold surface. 48…”

Strong Coupling, Hyperbolic Metamaterials and Optical Tamm States in Layered Dielectric-Plasmonic Media

“…Topological invariants of the photonic band structure in photonic crystals and in plasmonic materials coupled with photonic crystals, as the Zak phase play an important role in the edge state properties (Xiao et al, 2014(Xiao et al, , 2015Gao et al, 2015;Henriques et al, 2020). Moreover, a requirement for the generation of edge states in crystals is the band inversion (Zak, 1989;Xiao et al, 2014Xiao et al, , 2015Esmann et al, 2018;Wang et al, 2019).…”

“…Up to date most of the optical Tamm states investigated are based either on structures made of two planar photonic crystals (Kavokin et al, 2005;Vinogradov et al, 2010;Xiao et al, 2014;Esmann et al, 2018), where one of them presents band inversion, or structures based on a photonic crystal and plasmonic materials (Durach and Rusina, 2012;Henriques et al, 2020), or an excitonic material (Núñez-Sánchez et al, 2016). Moreover, the analogy between photonic layered media and electronic lattices has been also extended to systems supporting mechanical waves (Xiao et al, 2015;Yang et al, 2016;Ma et al, 2019).…”

“…This is largely due the geometrical simplicity of the one-dimensional structures and the properties of the nearfields generated by the excitation of surface plasmon modes. Over the last decades planar layered stacks of noble metal films combined with dielectrics have been used in applications as refractive index sensors (Homola, 2008), structures for fluorescence decay engineering (Amos and Barnes, 1997;Barnes, 1998;Liebermann and Knoll, 2000), hyperbolic metamaterials (Cortes et al, 2012;Poddubny et al, 2013;Guo et al, 2020), strong-coupling between emitters and plasmon modes (Bellessa et al, 2004;Törmä and Barnes, 2014;Chikkaraddy et al, 2016), and the one-dimensional and twodimensional photonic topological insulators (Su et al, 1979;Kaliteevski et al, 2007;Wang et al, 2008;Obana et al, 2019;Henriques et al, 2020).…”