  We study the effect of laser driving on a minimal model for a hexagonal
two-dimensional material with broken inversion symmetry. Through the
application of circularly polarised light and coupling to a thermal free
electron bath, the system is driven into a nonequilibrium steady state with
asymmetric, nonthermal carrier populations in the two valleys. We show that, in
this steady state, interband superconducting correlations between electrons can
develop independent of the sign of the electron-electron interactions. We
discuss how our results apply, for example, to transition metal
dichalcogenides. This work opens the door to technological applications of
superconductivity in a range of materials that were hitherto precluded from it.
