Topological plasmonic waveguides in triharmonic metal gratings.

We study topological surface-plasmon-polaritons at optical frequencies in tri-harmonic diffraction gratings formed at a metal-dielectric interface. The latter are shown to well approximate a bipartite Kronig-Penney model. Topologically protected localised modes are then predicted to occur at the edges of the grating and at defects formed by the combination of two mirror antisymmetric corrugations, whose bulk invariant is a step-wise varying Zak phase in both cases. An interesting special case wherein the defect state is in-fact forbidden is also observed that reveals the fragility of such states despite their topological nature.

A bipartite Kronig-Penney model with Dirac-delta potential scatterers.

Here we present a simple extension to the age-old Kronig-Penney model, which is made to be bipartite by varying either the scatterer separations or the potential heights. In doing so, chiral (sublattice) symmetry can be introduced. When such a symmetry is present, topological chiral symmetry protected edge states are seen to exist in correspondence with the standard quantised Zak phase bulk invariant. This quantisation behaviour may also be observed within a 'gauge'-invariant on-diagonal matrix element of a unit eigenvalue equation. The solution proceeds through the conventional scattering formalism used to study the Kronig-Penney model, which does not require further tight-binding approximations or mapping into a Su-Schrieffer-Heeger model. The cases in which chiral symmetry is absent are then seen to not host topologically protected edge states, as verified by zero bulk invariants.