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.