High- - a negative-Uinterpretation of cuprate superconductivity, incorporating questions of crossover, micro-inhomogeneity and a compound order parameter

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Abstract
The two-subsystem, negative-U interpretation of high-temperature superconducting (HTSC) behaviour in the mixed-valent, square-planar cuprate metals is pursued further. The question of the symmetry of the order parameter is central to understanding the HTSC phenomenon. Many have by now examined the potentialities of a mixed order parameter to cope with the wealth of data of all types available from these materials. It is emphasized here that it is actually a mistake for the present mixed-valent, highly tight-binding systems to seek a single, spatially homogeneous, compound order parameter. The systems are demonstrably micro-inhomogeneous due to charge segregation as in many substituted systems very close to Mott localization. In these circumstances there is a fascinating interplay between magnetism, charge and structural aspects to the problem at the unit cell level. Questions of local moment seeding, of local trapping of carriers structurally and magnetically, of on-site Jahn - Teller and bonding distortions, on the one hand, are highly intertwined, on the other, with somewhat more delocalized aspects to the problem, like SDWs, CDWs, the resonant valence band state, etc. All these matters have to be treated simultaneously, in a way appropriate to the precise level of carrier doping secured. Control over the outcome is dependent, moreover, from system to system upon the detailed degree of covalency introduced into the problem by the particular counter-ions employed. The present review makes an attempt to hold together all the published information on a coherent basis. That basis is seen as being provided by a negative-U sequencing of state energies in the mixed-valent cuprates, once it is accepted that the systems are not homogeneous at the micro-level. Results on the LSCO system, for example, find interpretation in terms of moderately well organized discommensurations in charge and spin distribution. The fact that this approach has been followed from the beginnings of high-temperature superconduction, now nearly ten years ago, without any sustained discouragement from the accumulating data, indicates that it provides a means of interpretation worth more direct attention than it has received to date. In particular it provides very naturally a means to understand what it is that confines high-temperature superconduction to its narrow range - the square-planar, layered, mixed-valent cuprates. There is in essence only one high-temperature superconductor and this paper attempts again to say why.