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.

💡 Research Summary

This topical review provides a comprehensive overview of recent progress in mapping and interpreting collective electronic excitations—plasmons, excitons, intra‑ and interband transitions—in solids using momentum‑ and frequency‑resolved spectroscopies together with first‑principles many‑body perturbation theory. The authors begin by emphasizing that the dielectric function ε(q, ω) and its inverse ε⁻¹(q, ω) constitute the fundamental quantities whose zeros and poles encode the existence of collective modes. Plasmons appear as zeros of ε (or poles of ε⁻¹) and, within the random‑phase approximation, display a quadratic dispersion at small momentum. However, real materials exhibit strong deviations due to band‑structure anisotropy, local‑field effects, and coupling to interband continua. Excitons, on the other hand, arise from the electron‑hole kernel of the Bethe–Salpeter equation (BSE) and manifest as resonant poles in ε(ω). At finite q they acquire dispersion and can hybridize with plasmons or phonons, giving rise to mixed exciton‑plasmon or exciton‑phonon polaritons, especially in low‑dimensional or polar semiconductors.

The review then details the experimental pipeline for electron energy‑loss spectroscopy (EELS) and inelastic X‑ray scattering (IXS). Raw spectra must be corrected for multiple scattering, background subtraction, normalization, and Kramers–Kronig inversion, each step introducing uncertainties that can bias the extracted loss function L(q, ω)=−Im ε⁻¹(q, ω). To make sense of the often‑dense (q, ω) data, the authors introduce the concept of spectral band structures (SBS), which are essentially momentum‑energy maps of the dielectric response. Central to the paper is the multipole‑Padé approximant (MPA) methodology, denoted MPA(q), which expands ε(q, ω) and ε⁻¹(q, ω) as rational functions of both momentum and frequency. This analytical representation compresses large numerical datasets into a small set of parameters, enabling clear visualization of mode dispersions, avoided crossings, and hybridization strengths.

Illustrative case studies span simple metals, semiconductors such as ZnO, and a variety of low‑dimensional systems (graphene, transition‑metal dichalcogenides, van‑der‑Waals heterostructures). In metals, the MPA‑based SBS reveals anisotropic plasmon branches, strong Landau damping, and mode mixing with interband transitions that are invisible in a pure RPA picture. In ZnO, the SBS simultaneously captures plasmon renormalization and excitonic resonances, highlighting the quantitative gap between RPA and BSE predictions and demonstrating how post‑processing (e.g., alignment of experimental loss peaks with theoretical poles) can bridge theory and experiment. For 2D materials, reduced screening dramatically enhances exciton binding energies and promotes strong exciton‑plasmon coupling; the SBS clearly shows q‑dependent splitting and the emergence of mixed polaritonic branches.

The authors also discuss practical post‑processing strategies that improve quantitative agreement, such as deconvolution of multiple‑scattering contributions, background modeling, and systematic Kramers–Kronig procedures. They stress that accurate inclusion of local‑field effects (off‑diagonal G‑vectors in the dielectric matrix) is essential for reproducing fine features, especially in anisotropic crystals.

Finally, the review outlines open challenges: (i) the computational cost of fully self‑consistent GW+BSE calculations that include electron‑phonon coupling; (ii) experimental limitations in energy and momentum resolution, particularly at high energies where signal‑to‑noise ratios drop; (iii) the need for unified theoretical frameworks that treat electronic, ionic, and photonic degrees of freedom on equal footing, enabling predictive modeling of mixed modes without resorting to phenomenological coupled‑oscillator models. The authors suggest that machine‑learning‑assisted parameter fitting, real‑time evaluation of dynamic screening, and development of efficient diagrammatic techniques for multi‑mode coupling could address these hurdles.

In summary, by marrying state‑of‑the‑art momentum‑resolved spectroscopies with sophisticated first‑principles dielectric‑function calculations and introducing analytical SBS/MPA tools, the paper provides a powerful roadmap for quantitatively deciphering collective electronic excitations across a broad class of materials, thereby informing the design of plasmonic, excitonic, and polaritonic devices for next‑generation photonic and quantum technologies.