Codimension one foliations of flat $ 3$-manifolds

Abstract

A reliable estimate of the density of states having in-plane and out-of-plane symmetry in the O K-edge and the Cu L 3 -edge polarized spectra is important for checking the validity of several theoretical models which predict an active role for these states in the mechanism of superconductivity. In the present contribution, we report on our fluorescenceyield O K-edge and Cu L 3 -edge polarized spectra obtained for a well characterized and oriented overdoped Tl(2212) thin film as well as our simultaneous fluorescence-and total-yield Cu L 3 measurements on an optimally doped Tl(2212) thin film. Our results show that a significant number of out-of-plane O 2p z and Cu 3d z 2 −r 2 holes also exist in thallium cuprates, more so in the overdoped case, and that use of the bulk-sensitive fluorescence technique is better for obtaining a reliable estimate of the density and symmetry of these holes. The spectra are compared with those reported earlier for other cuprate systems and are interpreted in terms of the available band-structure calculations. No direct correlation between superconductivity and the presence or absence of out-of-plane covalent and doping hole densities appears plausible, so theories based on the existence of a large density of such holes appear to be inconsistent with the experiment.