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Superconductivity in Semiconductor Structures: the Excitonic Mechanism

We study theoretically the effect of the fermion and boson densities on the superconductivity transition critical temperature $(T_c)$ of a two dimensional electron gas (2DEG), where superconductivity is mediated by a Bose-Einstein condensate of exciton-polaritons. The critical temperature is found to increase with the boson density, but surprisingly it decreases with the 2DEG density increase. This makes doped semiconductor structures with shallow Fermi energies better adapted for observation of the exciton-induced superconductivity than metallic layers. For the realistic GaAs-based microcavities containing-doped and neutral quantum wells we estimate $T_c$ as close to 50K. Superconductivity is suppressed by magnetic fields of the order of 4T due to the Fermi surface renormalisation.