Excitonic insulators — where electron-hole pairs condense into a macroscopic quantum state — have been hunted in transition metal chalcogenides for years. The candidates share a feature: d-orbital electrons with strong Coulomb interactions. But a puzzle persists: the binding energies are large (suggesting high transition temperatures), yet the actual transition temperatures are low.
This paper explains the discrepancy. Using dynamical mean-field theory on two- and three-orbital Hubbard models, they show that on-site Coulomb repulsion U strongly suppresses the condensation temperature, especially at higher electron-hole pair densities. Without U, Tc grows with pair density at fixed inter-orbital interaction V. With U, it doesn't — more pairs doesn't mean higher Tc because the repulsion penalizes the on-site component of the condensate.
In the three-orbital model, competing electron-hole pairing channels provide additional suppression. Multiple orbital pairs want to condense simultaneously, and the competition between them reduces the temperature at which any single channel wins. An orbital-selective pairing state is identified — condensation in one channel while others remain normal. Strong binding energy and low transition temperature coexist because the same correlations that produce the binding also suppress the ordering.