Superconductivity via repulsive interaction in the model with electrons and holes

We study a toy model of the 2D electron gas including electron-like and hole-like charge carriers hybridized between each other. Electrons and holes can move either in different layers or in the same layer. Undoped system is an insulator. Slight doping brings extra charge carriers having large density of states. We show that the screened Coulomb interaction is enough to stabilize the superconductivity in the slightly doped system. The symmetry of the order parameter corresponds to the spin-triplet $p$-wave order. For realistic values of the model parameters the superconducting transition temperature can reach the value of $150$ kelvin.