Charge density response in layered metals: retardation effects, generalized plasma waves and their spectroscopic signatures

TL;DR

This paper investigates how anisotropy and retardation effects in layered metals alter plasma wave behavior, leading to mixed excitations and distinctive spectroscopic signatures beyond standard models.

Contribution

It derives a generalized density and current correlation framework for layered metals, revealing retardation effects and mixed plasma modes not captured by traditional RPA.

Findings

Retardation effects modify plasma mode dispersion in layered metals.

Mixed longitudinal-transverse excitations produce a double-peak in density response.

Spectroscopic signatures of these effects are accessible via electron-energy-loss and X-ray techniques.

Abstract

Transverse plasma polaritons and longitudinal plasmons describe the propagation of light-matter modes in an isotropic metal. However, in a layered metal the anisotropy of the bare electromagnetic response mixes the longitudinal and transverse excitations, making the distinction between polariton and plasmon blurred at small wavevectors, where retardation effects of the electromagnetic interactions become quantitatively relevant. In the usual Kubo approach for the linear response, this effect appears as a mixing between the density and the transverse current fluctuations, that requires to revise the standard RPA approach for density correlations where only the instantaneous Coulomb potential is included. In this paper we derive the general expression for the density and current correlation functions at long wavelength in a layered metal, showing that below a crossover scale set by the anisotropy of the plasma frequencies retardation effects make the dispersion of the generalized plasma modes different from the standard RPA result. In addition, the mixed longitudinal and transverse nature of these excitations reflects in a double-peak structure for the density response, that can be eventually accessed by means of high-momentum resolution electron-energy-loss or X-rays spectroscopies.