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A system where a Bose-Einstein condensate of exciton-polaritons coexists with a Fermi gas of electrons has been recently proposed as promising for realization of room-temperature superconductivity. In order to find the optimum conditions for exciton and exciton-polariton mediated superconductivity, we studied the attractive mechanism between electrons of a Cooper pair mediated by the exciton and exciton-polariton condensate. We also analyzed the gap equation that follows. We specifically examined microcavities with embedded n-doped quantum wells as well as coupled quantum wells hosting a condensate of spatially indirect excitons, put in contact with a two-dimensional electron gas. An effective potential of interaction between electrons was derived as a function of their exchanged energy ℏω,taking into account the retardation effect that allows two negatively charged carriers to feel an attraction. In the polariton case, the interaction is weakly attractive at long times, followed by a succession of strongly attractive and strongly repulsive windows. Strikingly, this allows high critical temperature solutions of the gap equation. An approximate three-steps potential is used to explain this result that is also obtained numerically. The case of polaritons can be compared with that of excitons, which realize the conventional scenario of high-Tc superconductivity where a large coupling strength accounts straightforwardly for the high critical temperatures. Excitons are less advantageous than polaritons but may be simpler systems to realize experimentally. It is concluded that engineering of the interaction in these peculiar Bose-Fermi mixtures is complex and sometimes counter-intuitive, but leaves much freedom for optimization, thereby promising the realization of high-temperature superconductivity in multilayered semiconductor structures.
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