Cumulant method for the exciton-phonon coupling

One of the big challenges of theoretical condensed matter physics is the description, understanding, and prediction of the correlation effects induced by the mutual interaction between particles on materials properties. In both electronic and optical spectra the Coulomb interaction and the electron-phonon coupling cause a renormalization of the energies and change of spectral weight. Most importantly, they induce a finite lifetime on the quasi-particle (QP) excitations and can lead to new structures, often called satellites. The latter are pure many body effects and can be linked to the coupling of excitations, also termed dynamical effects. Standard methods developed in the framework of many body perturbation theory namely GW and the Bethe-Salpeter equation (BSE) are often not able to capture this complex physics. Instead, approaches based on a picture of electron-boson coupling such as the cumulant expansion are promising for the description of plasmon and phonon satellites.

Motivated by the recent success of the cumulant expansion of the one particle Green’s function in the description of photoemission spectra, we generalized the cumulant approach to the evaluation of the electronic polarizability. In this way we provide a new full ab-initio tool to include dynamical effects beyond the standard BSE in the description of neutral excitations as measured in optical absorption, photoluminescence, electron energy loss and inelastic X-rays scattering spectroscopies. The developed approach is applied to the study of phonon sidebands in the absorption and photoluminescence spectra of monolayer BN.