Nonretarded edge plasmon-polaritons in anisotropic two-dimensional materials

Dionisios Margetis, Matthias Maier, Tobias Stauber, Tony Low, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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,. By the Wiener-Hopf method, we solve an integral equation for in some generality. The EPP dispersion relation comes from the elimination of a divergent limiting Fourier integral for 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).

Original languageEnglish (US)
Article number055201
JournalJournal of Physics A: Mathematical and Theoretical
Issue number5
StatePublished - Jan 8 2020

Bibliographical note

Publisher Copyright:
© 2020 IOP Publishing Ltd.


  • Maxwells equations
  • Wiener-Hopf method
  • anisotropic conductivity
  • dispersion relation
  • edge plasmon polariton
  • quasi-electrostatic approximation
  • two-dimensional topological materials

How much support was provided by MRSEC?

  • Shared

Reporting period for MRSEC

  • Period 6


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  • MRFN

    Lodge, T.


    Project: Research project

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