We study a two-orbital attractive Hubbard model with a repulsive Hund's exchange coupling $J$ as an idealized model for a two-band superconductor. This framework is motivated by systems where strong isotropic electron-phonon coupling drives the on-site Hubbard repulsion $U$ to negative while leaving the exchange term unaffected. We solve the model at zero temperature and half filling using dynamical mean-field theory, focusing on the intraorbital singlet superconducting phase and discarding other possible instabilities, such as interorbital pairing and charge-density wave ordering. Already at $J=0$, the two-orbital model features a superconductor-insulator transition as $\left|U\right|$ grows, in contrast to the single-orbital case, which remains superconducting for any $U<0$. We find that a finite $J$ strengthens the effect of the attractive $U$, both in the normal state and, even more significantly, in the superconducting state. However, this pushes the system towards an effectively stronger coupling and hence to a faster transition to the insulating state. Similar to the Mott transition in the repulsive model, the superconductor-insulator transition here is marked by a vanishing quasiparticle weight $Z$. This leads to a scenario that recalls strongly correlated superconductivity close to a Mott transition, where pairing is enhanced but phase coherence is rapidly lost, even though the present model is dominated by attractive interactions.

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• Electron-phonon coupling
• Multiband superconductivity
• Mott insulators
• Strongly correlated systems
• Dynamical mean field theory
• Hubbard model
• Superconductivity