A nodeless superconducting (SC) gap was reported in a recent scanning tunneling spectroscopy experiment of a copper-oxide monolayer grown on a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) substrate [Zhong et al., Sci. Bull. 61, 1239 (2016)], which is in stark contrast to the nodal $d$-wave pairing gap in the bulk cuprates. Motivated by this experiment, we first show with first-principles calculations that the tetragonal CuO (T-CuO) monolayer on the Bi2212 substrate is more stable than the commonly postulated ${\mathrm{CuO}}_2$ structure. The T-CuO monolayer is composed of two ${\mathrm{CuO}}_2$ layers sharing the same O atoms. The band structure is obtained by first-principles calculations, and its strong electron correlation is treated with the renormalized mean-field theory. We argue that one ${\mathrm{CuO}}_2$ sublattice is hole doped while the other sublattice remains half filled and may have antiferromagnetic (AF) order. The doped Cu sublattice can show $d$-wave SC; however, its proximity to the AF Cu sublattice induces a spin-dependent hopping, which splits the Fermi surface and may lead to a full SC gap. Therefore, the nodeless SC gap observed in the experiment could be accounted for by the $d$-wave SC proximity to an AF order, thus it is extrinsic rather than intrinsic to the ${\mathrm{CuO}}_2$ layers.

• Received 20 July 2017
• Revised 27 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.035112