based on a Lieb-lattice model

For the newly discovered cuprate superconductor Ba₂CuO_3+δ, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient CuO₂ planes [1]. We first show that the Lieb-lattice structure is nearly as stable as the chain-type structure known to exist as e.g. Sr₂CuO₃. Then we construct a multiorbital Hubbard model based on first-principles calculation, and apply the fluctuation-exchange approximation. We show that s-wave and d-wave pairings closely compete with each other and, more interestingly, that a coexistence of intra- and interorbital pairings arises. We also reveal an intriguing relation of the Lieb model with the two-orbital model for the usual K₂NiF₄-type cuprate where a close competition between s- and d-wave pairings is known to occur. We further show that s±-wave superconductivity is strongly enhanced when the d_3z2−r2 band is raised in energy so that it becomes nearly “incipient” with the lower edge of the band close to the Fermi level within a realistic band filling regime. The enhanced superconductivity in the present model is in fact shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.
[1] K. Yamazaki et al., Phys. Rev. Res. 2, 033356 (2020).