Electronic-geometric relationships in copper-oxide-based superconductors

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 CuII 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 x²-y² band begins to empty. The 1:2:3 compound is more complex, but an orbital model is developed to follow the change in CuII charge density with both oxygen stoichiometry in YBa₂Cu₃O_7-δ and also the geometrical changes with temperature and stoichiometry. The focus is on the details of electron transfer to the CuIII chains. As indicated by tight-binding calculations, the relative placement of the x²-y² bands of CuII and the z²-y² band of CuIII is a sensitive function of the Cu-O distance and the puckering of the CuII{O}²$ sheets. For ${δ}=0$ 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 ${Cu}II$ and ${Cu}III$. For ${δ}=0$ 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 ${δ}{~}0.6$, 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 ${Cu}IIO₂ sheets has similar orbital origins to the tetragonal-to-orthorhombic distortion of the 2:1:4 compound. Some structural alternatives are examined for the 1:2:3 stoichiometry using similar ideas. KY₂{Cu}₃O₇ and AgLa₂{Cu}₃O₇ might be possible synthetic goals for a material with the same stoichiometry as the 1:2:3 compound but with a different structure. For the 1:2:4 compound YBa₂{Cu}₄O₈, which contains double chains in place of the single chains found in the 1:2:3 system, some of the copper atoms have to have nonintegral oxidation states. We show that a striking feature of the electronic structure is how the geometry of the system naturally allows such a process to happen. The recently made material Pb₂Sr₂(R_1-yMyII)Cu₃O₈₊ₓ(2:2:1:3) (R is defined as one of the lanthanide elements and MII is a divalent metal) exhibits structural-electronic features found in the 1:2:3 and in the 2:1:4 systems. Using the simple electronic ideas developed earlier it is suggested that there may be two regions where superconductivity should be observed, one for low and one for high x.