Spectral fingerprints of electron-plasmon coupling

We investigate the spectroscopic fingerprints of electron-plasmon coupling in integrated (PES) and angle-resolved photoemission spectroscopy (ARPES). To account for electron-plasmon interactions at a reduced computational cost, we derived the plasmonic polaron model, an approach based on the cumulant expansion of many-body perturbation theory that circumvents the calculation of the $GW$ self-energy. Through the plasmonic polaron model, we predict the complete spectral functions and the effects of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Si, Ge, and GaAs exhibit well-defined plasmonic polaron band structures, i.e., broadened replica of the valence bands redshifted by the plasmon energy. Based on these results, (i) we assign the structures of the plasmon satellite of silicon (as revealed by PES experiments) to plasmonic Van Hove singularities occurring at the $L$, $\mathrm{\Omega }$, and $X$ high-symmetry points and (ii) we predict the ARPES signatures of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Overall, the concept of plasmonic polaron bands emerges as a new paradigm for the interpretation of electronic processes in condensed matter, and the theoretical approach presented here provides a computationally affordable tool to explore its effect in a broad set of materials.

Figure 1

Angle-resolved spectral function of silicon for momenta along the $\mathrm{\Gamma }\text{−}X$ direction evaluated from (a) the plasmonic polaron model [Eq. (5)] and (b) converged $\mathrm{S}GW+{\text{C}}_{\mathrm{AHK}}$ calculations from Ref. [15]. The vertical arrow indicates the plasmon energy ${\mathrm{\Omega }}_p$ of silicon. The bare PBE band structure and its shifted plasmonic polaron replica are shown in blue.

Figure 2

(a) Spectral function of silicon determined from the plasmonic polaron model [Eq. (5)]. The plasmonic polaron intensity has been magnified by a factor of 3 to enhance visibility. (b) Experimental (integrated) x-ray photoemission spectrum (XPS) of silicon reproduced from Ref. [18]. (c) Quasiparticle and plasmonic polaron (magnified by a factor of 2) density of states (DOS). Different peaks and shoulders of the plasmonic polaron resonance in the XPS spectrum are attributed to plasmonic Van Hove singularities occurring on different high-symmetry lines in the Brillouin zone (red circles).

Figure 3

Spectral function of (a) Ge and (c) GaAs determined from the plasmonic polaron model [Eq. (5)]. The plasmonic polaron intensity has been magnified by a factor of 3 to enhance visibility. $\alpha$, $\beta$, and $\gamma$ denote regions characterized by low density of states due to the absence of plasmonic polarons and quasiparticle states. Panels (b) and (d): quasiparticle and plasmonic polaron DOS of Ge and GaAs.

Figure 4

Spectral function (a) and DOS (b) of diamond determined from the plasmonic polaron model [Eq. (5)].