Photonic Chern insulators from two-dimensional atomic lattices interacting with a single surface plasmon polariton

We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having resonant atomic transitions to excited states with different angular momentum. We employ a computational method based on the recently proposed Dirichlet-to-Neumann (DtN) map technique which accurately models non-Markovian dynamics as well as interactions involving higher-order electric and magnetic multipole transitions. We design topologically robust edge states which are used to achieve unidirectional emission and non-reciprocal transmission of single photons. We also point out the challenges in realizing bands with higher Chern numbers in such systems.