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 ${x}^{2}\ensuremath{-}{y}^{2}$ 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 $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ 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 ${x}^{2}\ensuremath{-}{y}^{2}$ bands of ${\mathrm{Cu}}^{\mathrm{II}}$ and the ${z}^{2}\ensuremath{-}{y}^{2}$ band of ${\mathrm{Cu}}^{\mathrm{III}}$ is a sensitive function of the Cu-O distance and the puckering of the ${\mathrm{Cu}}^{\mathrm{II}}$${\mathrm{O}}^{2}$ sheets. For $\ensuremath{\delta}=0$ in the observed structure, the two bands overlap such that charge transfer to the chains is allowed, but at the same time the integrity of the two types of copper atoms is maintained as ${\mathrm{Cu}}^{\mathrm{II}}$ and ${\mathrm{Cu}}^{\mathrm{III}}$. For $\ensuremath{\delta}=0$ in the idealized structure where the planes are not puckered and all Cu-O distances are set equal, the two bands overlap so much that this integrity is lost. For $\ensuremath{\delta}\ensuremath{\sim}0.6$, after the $c$-axis anomaly has shortened the Cu(1)-O(1) distance, charge transfer is completely switched off. At this point ${T}_{c}$ is seen experimentally to rapidly drop. Our major finding is that the details of the electronic structure are crucially dependent upon the geometry. We show how the puckering of the ${\mathrm{Cu}}^{\mathrm{II}}$${\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 1:2:3 stoichiometry using similar ideas. K${\mathrm{Y}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and Ag${\mathrm{La}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ 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 Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$, 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 ${\mathrm{Pb}}_{2}{\mathrm{Sr}}_{2}({R}_{1\ensuremath{-}y}{M}_{y}^{\mathrm{II}}){\mathrm{Cu}}_{3}{\mathrm{O}}_{8+x}(2:2:1:3)$ ($R$ is defined as one of the lanthanide elements and ${M}^{\mathrm{II}}$ 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 $x$.
Search from 250 M+ research papersSearch from 250 M+ research papers
Jul 13, 2012
R.L Prasad + 2
