  We study high-density electron-hole (e-h) systems with the electron density
slightly larger than the hole density. We find a new superconducting phase, in
which the excess electrons form Cooper pairs moving in an e-h BCS phase. The
coexistence of the e-h and e-e orders is possible because e and h have opposite
charges, whereas analogous phases are impossible in the case of two fermion
species that have the same charge or are neutral. Most strikingly, the e-h
order enhances the superconducting e-h order parameter by more than one order
of magnitude as compared with that given by the BCS formula, for the same value
of the effective e-e attractive potential \lambda^{ee}. This new phase should
be observable in an e-h system created by photoexcitation in doped
semiconductors at low temperatures.
