Bulk plasmons in elemental metals

TL;DR

This study addresses bulk plasmons in 25 elemental metals by computing the frequency- and momentum-dependent inverse dielectric function $Y(q,omega)$ from first principles within the random-phase approximation and by introducing a generalized MPA(q) model to represent the dielectric response. The authors map detailed spectral band structures, reveal complex, anisotropic, and multi-pole plasmonic features, and demonstrate good agreement with optical-limit experiments. A key contribution is the MPA(q) framework, which provides a compact, physically motivated description of $Y(q,omega)$ across momentum and frequency and offers a practical starting point for GW/BSE calculations. The work establishes a reference for plasmonics and spectroscopy in elemental metals and can guide both fundamental studies and applications in plasmonics.

Abstract

The spectral properties, momentum dispersion, and broadening of bulk plasmonic excitations of 25 elemental metals are studied from first principles calculations in the random-phase approximation. Spectral band structures are constructed from the resulting momentum- and frequency-dependent inverse dielectric function. We develop an effective analytical representation of the main collective excitations in the dielectric response, by extending our earlier model based on multipole-Padé approximants (MPA) to incorporate both momentum and frequency dependence. With this tool, we identify plasmonic quasiparticle dispersions exhibiting complex features, including non-parabolic energy and intensity dispersions, discontinuities due to anisotropy, and overlapping effects that lead to band crossings and anti-crossings. We also find good agreement between computed results and available experiments in the optical limit. The results for elemental metals establish a reference point that can guide both fundamental studies and practical applications in plasmonics and spectroscopy.

Figures (10)

• Figure 1: Spectral contributions of the intra-band (dashed orange line), the inter-band (dash-dotted blue line), and the plasma (solid green line) frequency as a function of energy, evaluated with Eqs. \ref{['eq:intra_freq']}, \ref{['eq:inter_freq']}, and \ref{['eq:plasma_freq']}, respectively. The total area under the plasma curve is filled with each corresponding contribution.
• Figure 2: Comparison of the computed RPA loss function of V (a), Cu (b), and Zn (c) in the optical limit, with experimental EELS data from Ref. eels_atlas, REELS from Ref. Werner2009JPCRD and theoretical IPA calculations from Ref. Werner2009JPCRD.
• Figure 3: Real (a) and imaginary (b) parts of the inverse dielectric function of V computed with RPA in the optical limit. The numerical data is compared with its corresponding MPA model with $n_Y=13$ poles. Dashed lines in the bottom panel represent the individual contributions of each pole. The most prominent pole is highlighted with a gray filling.
• Figure 4: (a) Relation between the effective number of electrons, $Z_{\mathrm{eff}}$, and the number of valence electrons, $Z_{\mathrm{val}}$, listed in Table \ref{['tab:metals']} for the set of studied metals. $Z_{\mathrm{eff}}$ is computed from the energy position of the main MPA pole, with Eq. \ref{['eq:Zeff']}. The black dashed line represents the identity relation. (b) Relation between the spectral weight, $\mathrm{Re}[2 R]$, and the energy position, $\mathrm{Re}[\Omega]$, of the main MPA pole of all the studied metals. The black dashed line corresponding to $\mathrm{Re}[2 R]=\mathrm{Re}[\Omega]$, represents the ideal PPA model where all the spectral weight is concentrated in a single pole. The presence of other poles with significant spectral weights lowers the position with respect to this PPA line. The gray dashed line represents a pole with half the spectral weight.
• Figure 5: Spectral band structures corresponding to the RPA loss function, $|\mathrm{Im} [Y (\omega, {\mathbf q})]|$, of cubic elemental metals from rows II-IV of the periodic table. The plots are made for two high-symmetry ${\mathbf q}$-lines of bulk Li (a), Na (b), Al (c), K (d), and Ca (e).