Nodeless high-T${}_c$ superconductivity in highly-overdoped monolayer CuO${}_2$

We study the electronic structure and superconductivity in CuO${}_2$ monolayer grown recently on $d$-wave cuprate superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$. Density functional theory calculations indicate significant charge transfer across the interface such that the CuO${}_2$ monolayer is heavily overdoped into the hole-rich regime yet inaccessible in bulk cuprates. We show that both the Cu $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals become important and the Fermi surface contains one electron and one hole pocket associated with the two orbitals respectively. Constructing a minimal correlated two-orbital model for the $e_g$ complex, we show that the spin-orbital exchange interactions produce a nodeless superconductor with extended $s$-wave pairing symmetry and a pairing energy gap comparable to the bulk $d$-wave gap, in agreement with recent experiments. The findings point to a direction of realizing new high-$T_c$ superconductors in ozone grown transition-metal-oxide monolayer heterostructures.