Electron-phonon coupling within Quasiparticle Self-consistent GW

There is clear evidence that standard Density Functional Theory (DFT) understimates electron-phonon coupling interaction in many materials, including even simple sp-bonded compounds. Hybrid functionals and quasiparticle GW corrections suggest that nonlocal exchange-correlation enhances the electron-phonon interaction as a consequence of an improved description of the electronic screening. This has highlighted the need to move beyond local exchange-correlation functionals within DFT, but complete field-theoretic investigations are still missing. In this talk I will introduce the development of a field-theoretic methodology which is able to predict on an equal footing electronic quasiparticles and phonons as well as their interaction. Such an approach has been implemented within the Quasiparticle Self-consistent GW (QSGW) formalism which describes well the electronic properties for a wide range of materials, including many where standard DFT fails.