Dynamical Phonon Screening of Excitons from First Principles without Frequency via the Dyson Supermatrix

Recently, we introduced a novel ab initio approach to calculate the effect of dynamical phonon screening and phonon-driven dissociation of excitons in optoelectronic materials [1, 2]. In this talk, we will present a rigorous theoretical framework to efficiently incorporate the frequency dependent phonon-screened electron-hole interaction kernel within the ab initio Bethe-Salpeter equation for periodic extended systems using the Dyson supermatrix, an upfolded matrix containing all electronic and vibrational degrees of freedom [3]. We will show how this formalism is exactly equivalent to self-consistent solution of the frequency-dependent quasiparticle equation and will demonstrate how to construct ‘upfolded’ Dyson supermatrices for periodic extended systems that correctly conserve crystal momentum in virtual scattering processes. Within this formalism, I will show how specific intermediate states involved in virtual electron-phonon scattering processes can be identified and will highlight the nature of the approximations implicitly assumed in perturbative self-energy expansions. We will subsequently apply this formalism to compute phonon screened exciton binding energies and scattering rates, presenting a comparison with converged self-consistent and ‘single-shot’ perturbative approaches.



[1] Alvertis, Haber, Li, Coveney, Louie, Filip & Neaton, PNAS 121, e2403434121 (2024).



[2] Coveney, Haber, Alvertis, Neaton & Filip, PRB 110, 054307 (2024).



[3] Coveney, Gant, Haber, Alvertis, Neaton & Filip, In prep. (2024).