Berlin 2024 – scientific programme

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O: Fachverband Oberflächenphysik

O 44: 2D Materials III: Electronic Structure (joint session O/TT)

O 44.1: Talk

Wednesday, March 20, 2024, 10:30–10:45, MA 005

Semiclassical theory for plasmons in inhomogeneous two-dimensional systems — •Tjacco Koskamp, Koen Reijnders, and Mikhail Katsnelson — Radboud University, Nijmegen, The Netherlands

We construct a general theory for plasmons in inhomogeneous two-dimensional systems. Plasmons, quantized collective oscillations of conduction electrons in solids, can be used to manipulate and control light. This requires heterostructures of nanometer size, which are by definition spatially inhomogeneous, and difficult to describe analytically. Here, we present a novel semi-analytical method to describe plasmons in two-dimensional inhomogeneous media within the framework of the Random Phase Approximation (RPA). Our approach [1] is based on the semiclassical approximation, which is formally applicable when the length scale of the inhomogeneity is much larger than the plasmon wavelength. Within this framework, we obtain a classical Hamiltonian that describes the dynamics of quantum plasmons, given by the Lindhard function with spatially varying parameters. The classical trajectories generated by this Hamiltonian can be viewed as the analog of rays in geometrical optics. By subsequently adding the wave-like character of the plasmons to these classical trajectories, we can describe, for instance, plasmon scattering and plasmonic bound states. As an example, we compute the differential cross section for plasmon scattering by a radially symmetric impurity.

[1] T. M. Koskamp, M. I. Katsnelson, K. J. A. Reijnders, Phys. Rev. B 108, 085414 (2023)

Keywords: Plasmon; Semiclassical approximation; Random phase approximation; Plasmonics; 2D materials