This talk addresses the derivation of dispersion relations for fine-scale electromagnetic waves, the edge plasmon-polaritons, that can plausibly propagate along the edges of flat 2D materials. These materials may include purely anisotropic and hyperbolic materials (e.g., black phosphorus) and Dirac materials such as monolayer transition metal dichalcogenides. Our methodology invokes the theory of the Wiener-Hopf integral equations for the components of the electric field tangential to the conducting material. In this context, we will discuss the special role of Krein’s index for the existence of the dispersion relation, and some of the related physical implications.
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