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By an integral equation approach to the time-harmonic classical Maxwellequations, we describe the dispersion in the nonretarded frequency regime ofthe edge plasmon-polariton (EPP) on a semi-infinite flat sheet. The sheet hasan arbitrary, physically admissible, tensor valued and spatially homogeneousconductivity, and serves as a model for a family of two-dimensional conductingmaterials. We formulate a system of integral equations for the electric fieldtangential to the sheet in a homogeneous and isotropic ambient medium. We showhow this system is simplified via a length scale separation. This view entailsthe quasi-electrostatic approximation, by which the tangential electric fieldis replaced by the gradient of a scalar potential, $\varphi$. By theWiener-Hopf method, we solve an integral equation for $\varphi$ in somegenerality. The EPP dispersion relation comes from the elimination of adivergent limiting Fourier integral for $\varphi$ at the edge. We connect theexistence, or lack thereof, of the EPP dispersion relation to the index forWiener-Hopf integral equations, an integer of topological character. Weindicate that the values of this index may express an asymmetry due to thematerial anisotropy in the number of wave modes propagating on the sheet awayfrom the edge with respect to the EPP direction of propagation. We discussextensions such as the setting of two semi-infinite, coplanar sheets. Ourtheory forms a generalization of the treatment by Volkov and Mikhailov (1988Sov. Phys. JETP 67 1639).

Nonretarded edge plasmon-polaritons in anisotropic two-dimensional materials