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Transverse plasma polaritons and longitudinal plasmons describe thepropagation of light-matter modes in an isotropic metal. However, in a layeredmetal the anisotropy of the bare electromagnetic response mixes thelongitudinal and transverse excitations, making the distinction betweenpolariton and plasmon blurred at small wavevectors, where retardation effectsof the electromagnetic interactions become quantitatively relevant. In theusual Kubo approach for the linear response, this effect appears as a mixingbetween the density and the transverse current fluctuations, that requires torevise the standard RPA approach for density correlations where only theinstantaneous Coulomb potential is included. In this paper we derive thegeneral expression for the density and current correlation functions at longwavelength in a layered metal, showing that below a crossover scale set by theanisotropy of the plasma frequencies retardation effects make the dispersion ofthe generalized plasma modes different from the standard RPA result. Inaddition, the mixed longitudinal and transverse nature of these excitationsreflects in a double-peak structure for the density response, that can beeventually accessed by means of high-momentum resolution electron-energy-lossor X-rays spectroscopies.

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