Combining electron-phonon and dynamical mean-field theory calculations of correlated materials: Transport in the correlated metal Sr2RuO4

Electron-electron (e-e) and electron-phonon (e-ph) interactions are challenging to describe in correlated materials, where their joint effects govern unconventional transport, phase transitions, and superconductivity. Here we combine first-principles e-ph calculations with dynamical mean-field theory (DMFT) as a step toward a unified description of e-e and e-ph interactions in correlated materials. We compute the e-ph self-energy using the DMFT electron Green's function and combine it with the e-e self-energy from DMFT to obtain a Green's function including both interactions. This approach captures the renormalization of quasiparticle dispersion and spectral weight on equal footing. Using our method, we study the e-ph and e-e contributions to the resistivity and spectral functions in the correlated metal Sr2RuO4. In this material, our results show that e-e interactions dominate transport and spectral broadening in the temperature range we study (50-310 K), while e-ph interactions are relatively weak and account for only ∼10% of the experimental resistivity. We also compute effective scattering rates and find that the e-e interactions result in scattering several times greater than the Planckian value kBT, whereas e-ph interactions are associated with scattering rates lower than kBT. Our work demonstrates a first-principles approach to combine electron dynamical correlations from DMFT with e-ph interactions in a consistent way, advancing quantitative studies of correlated materials.