Proximity induced superconductivity in monolayer CuO${}_2$ on the cuprate substrates

To understand the recently observed high temperature superconductivity in the monolayer CuO${}_2$ grown on the Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ substrates, we propose a two band model of the hybridized oxygen $p_x$ and $p_y$ orbitals with the proximity effect of the substrate. We demonstrate that both the nodal and nodeless d-wave superconducting states can be induced by the proximity effect, depending on the strengths of the pairing parameters.