Topology in a one-dimensional plasmonic crystal

TL;DR

This paper investigates the topological properties of plasmonic bands in a graphene-metallic grating crystal, deriving models to identify topological phases and proposing experimental observation methods.

Contribution

It introduces a tight-binding model for plasmonic bands resembling the SSH Hamiltonian with energy-dependent hopping, enabling topological analysis.

Findings

Identification of topological and trivial phases controlled by the graphene-grating distance

Derivation of a Kronig-Penney type equation for plasmonic bands

Proposal of a scattering experiment to observe topological states

Abstract

In this paper we study the topology of the bands of a plasmonic crystal composed of graphene and of a metallic grating. Firstly, we derive a Kronig-Penney type of equation for the plasmonic bands as function of the Bloch wavevector and discuss the propagation of the surface plasmon polaritons on the polaritonic crystal using a transfer-matrix approach considering a finite relaxation time. Second, we reformulate the problem as a tight-binding model that resembles the Su-Schrieffer-Heeger (SSH) Hamiltonian, one difference being that the hopping amplitudes are, in this case, energy dependent. In possession of the tight-binding equations it is a simple task to determine the topology (value of the winding number) of the bands. This allows to determine the existense or absence of topological end modes in the system. Similarly to the SSH model, we show that there is a tunable parameter that induces topological phase transitions from trivial to non-trivial. In our case, it is the distance d between the graphene sheet and the metallic grating. We note that d is a parameter that can be easily tuned experimentally simply by controlling the thickness of the spacer between the grating and the graphene sheet. It is then experimentally feasible to engineer devices with the required topological properties. Finally, we suggest a scattering experiment allowing the observation of the topological states.