Semiclassical theory for plasmons in two-dimensional inhomogeneous media
preprintposted on 2023-03-11, 17:01 authored by T. M. Koskamp, M. I. Katsnelson, K. J. A. Reijnders
The progress in two-dimensional materials has led to rapid experimental developments in quantum plasmonics, where light is manipulated using plasmons. Although numerical methods can be used to quantitatively describe plasmons in spatially inhomogeneous systems, they are limited to relatively small setups. 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 is based on the semiclassical approximation, which is formally applicable when the length scale of the inhomogeneity is much larger than the plasmon wavelength. We obtain an effective classical Hamiltonian for quantum plasmons by first separating the in-plane and out-of-plane degrees of freedom and subsequently employing the semiclassical Ansatz for the electrostatic plasmon potential. We develop a theory for scattering of plasmons by radially symmetric inhomogeneities, and compute the total and differential scattering cross section for a specific model of the inhomogeneity.