Bulk-edge correspondences for surface plasmon polaritons: A circuit approach

In this study, we establish circuit-theoretical bulk-edge correspondences to indicate the existence of surface plasmon polaritons topologically. First, we reveal an essential topological transition in a minimal circuit model of a composite right-/left-handed transmission line. We then demonstrate that the circuit model can accurately explain the dielectric-metal transition. Using mirror symmetry and Foster's reactance theorem, we prove a parity-reactance correspondence that relates the parities of the bulk wave functions to the sign of the surface reactance. The parity-reactance correspondence describes the underlying mechanism of surface-plasmon-polariton formation without focusing on the Zak phase. Zero flat bands play an essential role in this mechanism, allowing us to define a topological integer that classifies the direct-current (DC) response. The conventional surface-reactance formula using the Zak phase requires plasmonic modification by the defined topological integer. Finally, we develop alternative bulk-edge correspondences based on the DC response without invoking mirror symmetry.