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Interacting Bose-Fermi systems play a central role in condensed matterphysics. Here, we analyze a novel Bose-Fermi mixture formed by a cavityexciton-polariton condensate interacting with a two-dimensional electronsystem. We show that that previous predictions of superconductivity [F.P.Laussy, Phys. Rev. Lett. 10, 104 (2010)] and excitonic supersolid formation[I.A. Shelykh, Phys. Rev. Lett. 14, 105 (2010)] in this system are closelyintertwined- resembling the predictions for strongly correlated electronsystems such as high temperature superconductors. In stark contrast to a largemajority of Bose-Fermi systems analyzed in solids and ultracold atomic gases,the renormalized interaction between the polaritons and electrons in our systemis long-ranged and strongly peaked at a tunable wavevector, which can berendered incommensurate with the Fermi momentum. We analyze the prospects forexperimental observation of superconductivity and find that criticaltemperatures on the order of a few Kelvins can be achieved in heterostructuresconsisting of transition metal dichalcogenide monolayers that are embedded inan open cavity structure. All optical control of superconductivity insemiconductor heterostructures could enable the realization of new deviceconcepts compatible with semiconductor nanotechnology. In addition thepossibility to interface quantum Hall physics, superconductivity andnonequilibrium polariton condensates is likely to provide fertile ground forinvestigation of completely new physical phenomena.

physical review. b./physical review. b

Superconductivity and other phase transitions in a hybrid Bose-Fermi  mixture formed by a polariton condensate and an electron system in two  dimensions