Emergence of a condensate with finite-energy Cooper pairing in hybrid exciton/superconductor systems

We study theoretically a setup consisting of excitons formed in two valleys, with proximity-induced Cooper pairing, different in the conduction and valence bands. Due to the combination of a Coulomb interaction with superconducting proximity effects, Cooper pairing between electrons from conduction and valence bands from different valleys is formed. This finite-energy intervalley Cooper pairing has both even- and odd-frequency contributions. We show that there is a phase transition into the formation of a robust macroscopic condensate of such Cooper pairs and present characteristics of the corresponding Higgs modes.