  We show that optically pumped semiconductors can exhibit superconductivity.
We illustrate this phenomenon in the case of a two-band semiconductor
tunnel-coupled to broad-band reservoirs and driven by a continuous wave laser.
More realistically, we also show that superconductivity can be induced in a
two-band semiconductor interacting with a broad-spectrum light source. We
furthermore discuss the case of a three-band model in which the middle band
replaces the broad-band reservoirs as the source of dissipation. In all three
cases, we derive the simple conditions on the band structure, electron-electron
interaction, and hybridization to the reservoirs that enable superconductivity.
We compute the finite superconducting gap and argue that the mechanism can be
induced through both attractive and repulsive interactions and is robust to
high temperatures.
