Nonretarded edge plasmon-polaritons in anisotropic two-dimensional materials

Abstract

By an integral equation approach to the time-harmonic classical Maxwell equations, we describe the dispersion in the nonretarded frequency regime of the edge plasmon-polariton (EPP) on a semi-infinite flat sheet. The sheet has an arbitrary, physically admissible, tensor valued and spatially homogeneous conductivity, and serves as a model for a family of two-dimensional conducting materials. We formulate a system of integral equations for the electric field tangential to the sheet in a homogeneous and isotropic ambient medium. We show how this system is simplified via a length scale separation. This view entails the quasi-electrostatic approximation, by which the tangential electric field is replaced by the gradient of a scalar potential, $\phi$. By the Wiener-Hopf method, we solve an integral equation for $\phi$ in some generality. The EPP dispersion relation comes from the elimination of a divergent limiting Fourier integral for $\phi$ at the edge. We connect the existence, or lack thereof, of the EPP dispersion relation to the index for Wiener-Hopf integral equations, an integer of topological character. We indicate that the values of this index may express an asymmetry due to the material anisotropy in the number of wave modes propagating on the sheet away from the edge with respect to the EPP direction of propagation. We discuss extensions such as the setting of two semi-infinite, coplanar sheets. Our theory forms a generalization of the treatment by Volkov and Mikhailov (1988 Sov. Phys. JETP 67 1639).

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Cited by in corpus (8)

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• Theory of plasmonic edge states in chiral bilayer systems
• Edge plasmon-polaritons on isotropic semi-infinite conducting sheets
• Thresholdless excitation of edge plasmons by transverse current
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Drift velocity of edge magnetoplasmons due to magnetic edge channels
• Reduction of fully screened magnetoplasmons in a laterally confined anisotropic two-dimensional electron system to an isotropic one
• Exact theory of edge diffraction and launching of transverse electric plasmons at two-dimensional junctions