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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 5: Theoretical Aspects of Condensed Matter I

MP 5.3: Talk

Monday, March 18, 2024, 16:40–17:00, HL 102

Semiclassical quantization of quantum plasmons in spatially inhomogeneous media — •Koen Reijnders, Timur Tudorovskiy, and Mikhail Katsnelson — Radboud University, Institute for Molecules and Materials, Nijmegen, The Netherlands

We present a novel semi-analytical method to describe plasmons, collective excitations of the conduction electrons in solids, in spatially inhomogeneous media. Since these systems do not exhibit translational invariance, the Fourier transform cannot be used to construct a solution. However, when we demand that the characteristic scale of the inhomogeneities is much larger than the plasmon wavelength, we can instead employ techniques taken from the semiclassical approximation. In this way, we construct an asymptotic solution that is independent of the precise shape of the inhomogeneity [1]. Technically, we study a system of equations of motion that is equivalent to the random phase approximation, and which can also be viewed as a quantum generalization of the Vlasov--Poisson system. We solve this system self-consistently using the correspondence between quantum mechanical operators and classical observables on phase space. In this way, we obtain a classical Hamiltonian that describes the dynamics of quantum plasmons, given by the Lindhard function with spatially varying parameters. We then find the energy levels using Bohr--Sommerfeld quantization. Our results provide a theoretical basis to describe plasmonic waveguides and other setups in quantum plasmonics.

[1] K. J. A. Reijnders, T. Tudorovskiy, M. I. Katsnelson, Ann. Phys. (NY) 446, 169116 (2022)

Keywords: Semiclassical approximation; Bohr-Sommerfeld quantization; Plasmon; Waveguide; Random Phase Approximation