Electronic-geometric relationships in copper-oxide-based superconductors

Abstract

By using orbital ideas linking the dependence of the energies of the $d$ levels at copper sites with the details of the local coordination geometry it is shown through the use of tight-binding theory how the geometrical structure is crucial to the understanding of the electronic structure of copper-containing superconductors. Four systems are studied, the so-called 1:2:3, 1:2:4, 2:1:4, and 2:2:1:3 materials, from the viewpoint that superconductivity is only a possibility if the half-filled band situation at ${\mathrm{Cu}}^{\mathrm{II}}$ is destroyed by electron transfer. In the 2:1:4 compound this occurs largely via doping with, e.g., Sr. Here, we also examine the orthorhombic-to-tetragonal distortion of this compound and show by calculation how the driving force away from tetragonal decreases with strontium doping in accord with experiment. We show how this may be interpreted in terms of the changes in chemical bonding as the $x^2-y^2$ band begins to empty. The 1:2:3 compound is more complex, but an orbital model is developed to follow the change in ${\mathrm{Cu}}^{\mathrm{II}}$ charge density with both oxygen stoichiometry in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and also the geometrical changes with temperature and stoichiometry. The focus is on the details of electron transfer to the ${\mathrm{Cu}}^{\mathrm{III}}$ chains. As indicated by tight-binding calculations, the relative placement of the $x^2-y^2$ bands of ${\mathrm{Cu}}^{\mathrm{II}}$ and the $z^2-y^2$ band of ${\mathrm{Cu}}^{\mathrm{III}}$ is a sensitive function of the Cu-O distance and the puckering of the ${\mathrm{Cu}}^{\mathrm{II}}$ ${\mathrm{O}}^2$ sheets. For $\delta =0\mathrm{}$ in the observed structure, the two bands overlap such that charge transfer to the chains is allowed, but at the same time the integrity of the two types of copper atoms is maintained as ${\mathrm{Cu}}^{\mathrm{II}}$ and ${\mathrm{Cu}}^{\mathrm{III}}$. For $\delta =0\mathrm{}$ in the idealized structure where the planes are not puckered and all Cu-O distances are set equal, the two bands overlap so much that this integrity is lost. For $\delta \sim 0.6$, after the $c$-axis anomaly has shortened the Cu(1)-O(1) distance, charge transfer is completely switched off. At this point $T_c$ is seen experimentally to rapidly drop. Our major finding is that the details of the electronic structure are crucially dependent upon the geometry. We show how the puckering of the ${\mathrm{Cu}}^{\mathrm{II}}$ ${\mathrm{O}}_2$ sheets has similar orbital origins to the tetragonal-to-orthorhombic distortion of the 2:1:4 compound. Some structural alternatives are examined for the...