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arXiv · 1702.04925

Lippmann-Schwinger theory for two-dimensional plasmon scattering

Iacopo Torre·Mikhail I. Katsnelson·Alberto Diaspro·Vittorio Pellegrini·Marco Polini
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Abstract

Long-lived and ultra-confined plasmons in two-dimensional (2D) electron systems may provide a sub-wavelength diagnostic tool to investigate localized dielectric, electromagnetic, and pseudo-electromagnetic perturbations. In this Article, we present a general theoretical framework to study the scattering of 2D plasmons against such perturbations in the non-retarded limit. We discuss both parabolic-band and massless Dirac fermion 2D electron systems. Our theory starts from a Lippmann-Schwinger equation for the screened potential in an inhomogeneous 2D electron system and utilizes as inputs analytical long-wavelength expressions for the density-density response function, going beyond the local approximation. We present illustrative results for the scattering of 2D plasmons against a point-like charged impurity and a one-dimensional electrostatic barrier due to a line of charges. Exact numerical results obtained from the solution of the Lippmann-Schwinger equation are compared with approximate results based on the Born and eikonal approximations. The importance of nonlocal effects is finally emphasized.

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Iacopo Torre, Mikhail I. Katsnelson, Alberto Diaspro, Vittorio Pellegrini, Marco Polini. 2017-02-16. Lippmann-Schwinger theory for two-dimensional plasmon scattering. https://doi.org/10.1103/physrevb.96.035433

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