Cumulant Green's function calculations of plasmon satellites in bulk sodium: Influence of screening and the crystal environment

Abstract

We present ab initio calculations of the photoemission spectra of bulk sodium using different flavors of the cumulant expansion approximation for the Green's function. In particular, we study the dispersion and intensity of the plasmon satellites. We show that the satellite spectrum is much more sensitive to many details than the quasi-particle spectrum, which suggests that the experimental investigation of satellites could yield additional information beyond the usual studies of the band structure. In particular, a comparison to the homogeneous electron gas shows that the satellites are influenced by the crystal environment, although the crystal potential in sodium is weak. Moreover, the temperature dependence of the lattice constant is reflected in the position of the satellites. Details of the screening also play an important role; in particular, the contribution of transitions from 2s and 2p semi-core levels influence the satellites, but not the quasi-particle. Moreover, inclusion of contributions to the screening beyond the RPA has an effect on the satellites. Finally, we elucidate the importance of the coupling of electrons and holes by comparing the results of the time-ordered (TOC) and the retarded (RC) cumulant expansion approximations. Again, we find small but noticeable differences. Since all the small effects add up, our most advanced calculation yields a satellite position which is improved with respect to previous calculations by almost one eV. This stresses the fact that the calculation of satellites is much more delicate than the calculation of a quasi-particle band structure.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

“…A proven route to improve the plasmon description compared to GW is the cumulant expansion to the Green's function, which has been tested on Na, Al, graphene, Si, and the electron gas (Aryasetiawan et al, 1996; Guzzo et al, 2011; Gatti and Guzzo, 2013; Lischner et al, 2013, 2014; Caruso and Giustino, 2015, 2016; Caruso et al, 2015; Zhou et al, 2018). Based on an exponential ansatz, somewhat analogous to the coupled cluster expansion for the wave function, the cumulant Green's function for a hole takes the form (Aryasetiawan et al, 1996; Guzzo et al, 2011; Lischner et al, 2013)…”

Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm

“…The determinantal approach can be extended to other types of x-ray spectra besides XAS, such as X-ray photoemission spectroscopy (XPS) and resonant inelastic x-ray scattering (RIXS), using a similar linear algebra technique and search algorithm. It will be worthwhile to compare this new method with recent studies that apply a cumulant expansion to capture the charge-transfer satellites in XPS [61,62,100]. And it will be interesting to test the efficiency of the current approach to produce 2D RIXS spectra that provide rich information for materials characterization.…”

Insights into the electronic structure of OsO2 using soft and hard x-ray photoelectron spectroscopy in combination with density functional theory

“…To capture many-electron effects beyond DFT, many-body perturbation theory calculations using the GW+C approach were carried out. In recent years, the GW+C approach has been established as the state-of-the-art method to simulate photoemission spectra of bulk solids and nanomaterials with weak or moderate electron correlations [28][29][30][31][32][33][34][35][36]. Notably, this approach accurately describes both quasiparticle and plasmon satellite features in the electron spectral function, which is measured in photoemission experiments.…”