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

TL;DR

This study uses ab initio cumulant expansion methods to analyze plasmon satellites in bulk sodium, revealing their sensitivity to screening, crystal environment, and temperature, and improving satellite position predictions.

Contribution

It demonstrates the importance of detailed screening and crystal effects in accurately modeling plasmon satellites in sodium using cumulant Green's function methods.

Findings

Satellite spectra are more sensitive to details than quasiparticle spectra.

Including semi-core transitions and beyond-RPA screening improves satellite position accuracy.

Differences between time-ordered and retarded cumulant approaches are small but noticeable.

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 (QP) 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 (HEG) 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 QP. 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 QP band structure.