Abstract
We study a one-dimensional plasmonic system with non-trivial topology: a chain of metallic nanoparticles with alternating spacing, which is the plasmonic analogue to the Su-Schreiffer-Heeger model. We extend previous efforts by including long range hopping with retardation and radiative damping, which leads to a non-Hermitian Hamiltonian with frequency dependence. We calculate band structures numerically and show that topological features such as quantised Zak phase persist due to chiral symmetry. This predicts parameters leading to topologically protected edge modes, which allows for positioning of disorder-robust hotspots at topological interfaces, opening up novel nanophotonics applications.
Highlights
The rise of topological insulators, materials with an insulating bulk and conducting surface states that are protected from disorder, has inspired the study of analogous photonic and plasmonic systems.[12−23] Topological photonics shows exciting potential for unidirectional plasmonic waveguides,[24] lasing,[25] and field enhancing hotspots with robust topological protection, which could prove useful for nanoparticle arrays on flexible substrates.[26]
Plasmonic and photonic systems provide a powerful platform to examine topological insulators without the complication of interacting particles and with interesting additional properties like non-Hermiticity.[27−32] The lack of Fermi level simplifies the excitation of states, and the tunability made available by the larger scale allows for the study of disorder and defects in greater depth than electronic systems.[33−35] They simplify the study of topology in finite systems.[36]
We have presented a detailed study of the 1D topological plasmonic chain beyond the quasistatic limit
Summary
To the Bloch Hamiltonian, which is non-Hermitian and has frequency dependence. We calculate band structures and compare to the QS approximation, showing that the system is still topologically nontrivial because it shares eigenvectors with a chiral system. The zeros can only happen for the transverse case due to the third, long-range, term in the Green’s function in eq 7 The imaginary parts of the frequency when considering the topological nature of a non-Hermitian system.[78] Here the complex gap allows for the unambiguous identification of each band, which are labeled with different colors for clarity This permits the calculation of Zak phases. The presence of these imaginary parts suggest that it may be necessary to use an evanescent wave to excite the modes
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