Lippmann-Schwinger theory for two-dimensional plasmon scattering

Iacopo Torre, Mikhail I. Katsnelson, Alberto Diaspro, Vittorio Pellegrini, and Marco Polini
Phys. Rev. B 96, 035433 – Published 24 July 2017

Abstract

Long-lived and ultraconfined plasmons in two-dimensional (2D) electron systems may provide a subwavelength 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 nonretarded 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 pointlike 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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  • Received 16 February 2017

DOI:https://doi.org/10.1103/PhysRevB.96.035433

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Iacopo Torre1,2,*, Mikhail I. Katsnelson3, Alberto Diaspro4,5, Vittorio Pellegrini2, and Marco Polini2

  • 1NEST, Scuola Normale Superiore, I-56126 Pisa, Italy
  • 2Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
  • 3Radboud University, Institute for Molecules and Materials, NL-6525 AJ Nijmegen, The Netherlands
  • 4Optical Nanoscopy, Nanophysics, Istituto Italiano di Tecnologia, Via Morego 30, I-16163 Genova, Italy
  • 5Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, I-16146 Genova, Italy

  • *Iacopo.Torre@sns.it

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Issue

Vol. 96, Iss. 3 — 15 July 2017

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