# Lippmann-Schwinger theory for two-dimensional plasmon scattering

## TL;DR

This paper develops a comprehensive theoretical framework using the Lippmann-Schwinger equation to analyze 2D plasmon scattering in electron systems, incorporating nonlocal effects and comparing numerical and approximate solutions.

## Contribution

It introduces a general non-retarded scattering theory for 2D plasmons in both parabolic and Dirac systems, extending beyond local response approximations.

## Key findings

- Exact numerical solutions highlight nonlocal effects in plasmon scattering.
- Comparison shows limitations of Born and eikonal approximations.
- Framework applicable to various perturbations in 2D electron systems.

## 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.