Momentum- and frequency-resolved collective electronic excitations in solids: insights from spectroscopy and first-principles calculations

Collective electronic excitations, including plasmons, excitons, and intra- and interband transitions, play a central role in determining the dynamic screening, optical response, and energy transport properties of materials. Recent advances in momentum- and frequency-resolved spectroscopies, such as electron energy-loss spectroscopy (EELS) and inelastic x-ray scattering (IXS), together with progress in first-principles many-body perturbation theory (MBPT) calculations, now allow collective excitations to be mapped with considerable precision across the Brillouin zone. This topical review surveys current developments in the representation and interpretation of both experimental and theoretical dielectric-response spectra. Particular emphasis is placed on recent ways of representing spectral band structures (SBS) of the direct and inverse dielectric functions, such as analytical approaches based on multipole-Padé approximants in momentum and frequency (MPA($\q$)), which provide a combined band-like description of the dispersion of the main collective excitations. We discuss how features observed in metals, semiconductors, and low dimensional systems reflect the interplay between electronic structure, screening strength, and local-field effects, and how post-processing procedures can improve the quantitative comparison between experiment and theory. Finally, we provide perspectives on open challenges and potential developments in quantitative dielectric-function analyses.