Abstract
For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+\delta}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.
Highlights
More than 30 years have passed since the discovery of the high-Tc cuprates, but a full understanding of their physics remains one of the most challenging problems in the condensed matter physics [1]
We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K2NiF4 structure where a close competition between s- and d-wave pairings is known to occur
In an even wider scope, we reveal that the Lieb model has an intimate relation with the two-orbital model of the K2NiF4 structure where a close competition between s-wave and d-wave pairings is known to occur [9]
Summary
More than 30 years have passed since the discovery of the high-Tc cuprates, but a full understanding of their physics remains one of the most challenging problems in the condensed matter physics [1]. The cuprates have a layered perovskite crystal structure, where a copper atom is surrounded by oxygens, typically with an octahedral coordination. Since the octahedron is elongated in the c-axis direction, the crystal field splitting makes the 3dx2−y2 orbital have the highest energy among the 3d orbitals. The d9 electron configuration results in a situation where the electronic structure can be regarded as basically a single-band system. Some of the present authors have shown that there is a systematic material dependence, in which Tc is basically increased as the one-band character (3dx2−y2 ) becomes stronger, i.e., when the energy of the 3d3z2−r2 orbital is lowered below that of 3dx2−y2 , which is realized for higher apical oxygen heights [2,3,4,5]
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