Combining Electron-Phonon and Dynamical Mean Field Theory Calculations for Correlated Materials: Transport in the Correlated Metal Sr₂RuO₄

Electron-electron (e-e) and electron-phonon (e-ph) interactions combine in nontrivial ways in correlated materials, with their joint effects governing phenomena that range from transport to phase transitions and superconductivity. In this talk, we combine ab initio dynamical mean field theory (DMFT) and e-ph calculations to achieve a unified description of e-e and e-ph interactions in correlated electron systems. We apply this method to study the transport properties and spectral functions in the Hund's metal Sr₂RuO₄ (SRO), analyzing in detail the interplay of e-e and e-ph interactions. We show that the e-ph interactions in SRO are relatively weak, and account for only 10% of the resistivity when considered alone. However, when combined with DMFT, we find that e-ph interactions are significantly enhanced by the DMFT band renormalization, accounting for ∼30% of the resistivity in SRO for temperatures between 50 – 300 K. The resistivity computed with both e-e and e-ph interactions is in very good agreement with experiment, addressing the “missing resistivity” puzzle in SRO. We highlight two key differences between e-e and e-ph interactions in SRO: first, the e-e scattering exceeds the classical Planckian limit while e-ph scattering does not; second, the e-ph interactions show a significant momentum dependence, while the DMFT e-e interactions are local. Our results demonstrate a significant interplay of e-e and e-ph interactions in SRO beyond the Matthiessen’s rule.