Model high-temperature superconductors

Bond valence sum (BVS) analysis, developed by Brown (43) to calculate metal oxidation states in materials such as high-temperature superconductors and zeolites, has recently been shown by Thorp (44) to be predictive for metalloenzymes and model compounds. On the basis of crystallographic data, the empirical parameters r0 and B are determined. These values can then be used to calculate oxidation states from known coordination environments or coordination numbers from known oxidation states and bond lengths. The requisite equations are... 

Studies on other high-temperature superconductors Positron annihilation measurements across Tc, coupled with the calculations of PDD have been carried out in a variety of hole-doped superconductors that include YBa2Cu40g [48], Bi-Sr-Ca-Cu-0 [49], and Tl-Ba-Ca-Cu-0 [50, 51] systems. We will not labor with the details here, except to state that a variety of temperature dependencies are seen and these can be rationalized when the results are analysed in terms of positron density distribution and the electron-positron overlap function [39]. These calculations show that the positron s sensitivity to the superconducting transition arises primarily from the ability to probe the Cu-O network in the Cu-0 layer. The different temperature dependencies of lifetime, i.e., both the increase and decrease, can be understood in terms of a model of local electron transfer from the planar oxygen atom to the apical oxygen atom, after taking into account the correct positron density distribution within the unit cell of the cuprate superconductor. 

The MgO(OOl) surface has been the object of numerous studies because it is widely used as a substrate for the epitaxial growth of metals [36-38] and as a model support for dispersed small catalytic particles. It is also used as a substrate to grow high-temperature superconductors because of its close lattice match to YBa2Cu30v.x and its low chemical reactivity. 

As another example, this time drawn from the realm of classical thermodynamics, we may consider the thermal state of a neutron star, a high-temperature superconductor or a dense gas. In each case, there is little doubt as to the validity of thermodynamics itself On the other hand, if we wish to make progress in the description of the dense gas, for example, the laws of thermodynamics by themselves do not suffice. This is where modeling in fhe sense that it will be used primarily in this book comes in. In addition to the fundamental laws that apply to all thermodynamic systems, we must characterize those features of the problem that are nonuniversal. That is, we require an equation of state which has nowhere near the same level of generality as the laws of thermodynamics themselves. Again,... 

However Allen [641] and others have argued against an atomic interpretation. It is probably fair to say that atomic multiplet theory and the condensed matter models have not yet been completely reconciled. This question is important high temperature superconductors of the form RBa2Cu306, where R can be any member of the rare-earth series of elements except Ce and Pr, have attracted much attention. A fluctuation in valence involving 4/ electrons is likely to be involved in the emergence of high temperature superconductivity for these materials. 

Despite these limitations, minimization techniques are straightforward, robust and readily applicable, and can be applied to systems with large and complex unit cells. They are being used increasingly to refine approximate crystal structures and to calculate the relative energies of different polymorphs, as discussed later in this chapter and in Chapters 3 and 5. Highly complex structures may, moreover, now be modelled routinely as will be apparent in the discussion of silicates in Chapter 9 and high temperature superconductors in Chapter 10. 

The nature and energetics of electronic defects are major factors which control the properties of high-temperature superconductors. Atomistic simulation techniques allow an estimation of the formation energies of these defects. Within the framework of an ionic model, valence band holes are described in localized terms as Cu3 + (hCu) or 0 (h0) and defect electrons as Cu + (eCu)- The formation energy of these defects involves a contribution from the ionization potential/electron affinity of the appropriate ion in addition to a lattice energy term (including the effects of relaxation) and a band contribution, in the case of delocalized carriers (large polarons). 

The single-band ladder extension of the one-dimensional Hubbard model [18,19,22] has been utilized as a minimalist model to smdy spin-liquid behavior [11, 14, 43] and high-temperature superconductors [1, 5, 21, 25, 44]. The ladder model is a quasi-one-dimensional system with a fourfold degenerate Fermi surface and correlations in two-dimensions. 

Encouraged by these findings it is the aim of this report to study magnetic and transport phenomena of high-temperature superconductors probably in terms of the most simple effective one-band model describing both correlation and band structure effects, the so-called r-r -/model ... 

We also group materials of special interest, though they fall under the models a to c the defect concentrations in many insertion compoimds fall under model b . YBCO (YBa2Cu30J, a material which represents the high-temperature superconductors, draws much attention and its MIEC properties are intensively investigated. Its classification a to c ... 

---