Superconducting Behavior

Many of the properties of superconductors have been successfully accounted for by the Bardeen-Cooper-Schrieffer (BCS) microscopic theory of superconductivity. However, the theory cannot predict the occurrence of superconductivity in materials, i.e., it does not tell us what atomic constituents should be put together and what crystal system is necessary in order to obtain materials exhibiting high critical temperatures 7. However, prior to the advent of the BCS theory a large body of information regarding the occurrence of the superconductive state in elements, alloys, and intermetallic compounds was accummulated, notably by Matthias and his 

The BCS theory says that in the presence of an attractive interaction, electrons near the Fermi level having equal and opposite momentum and spin may attract each other to form pairs (known as Cooper pairs), resulting in the superconducting state. This attractive interaction involves the lattice of positive ions, i.e., is phonon induced. The paired superconducting state is at a lower energy and is separated from the normal-state energy by a finite gap. 

The term iV(0) can be computed from a knowledge of the coefficient of electronic contribution y to the heat capacity, determined from low-temperature heat capacity measurements. The Debye temperature 0 can also be determined from heat capacity data as 

The use of BCS theory to quantitatively compute for a given material requires detailed knowledge of both the electronic structure and the phonon spectrum. Information of this sort for complex materials (i.e., alloys and intermetallic compounds) is extremely difficult to obtain and one still relies on past experience and empiricism in the search for new materials. 

Clearly, electron concentration or density of states and the phonon spectrum are important factors determining the occurrence of superconductivity and emphasis on these factors will be placed in subsequent sections in discussing superconducting behavior. 

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This oxygen variation and the Cu oxidation states play a very important role in the superconducting behavior of this compound. For example, the oxygen content (or x vacancy), the copper oxidation states, and the onset temperatures for superconductivity are listed below for different compositions. 

Substitution of other transition metal ions for Cu, however, was observed (174) to be highly deleterious to superconducting behavior. Table 14 shows the results of 10% metal-ion substitution in the Cu sites. 

In addition to the zero resistivity, superconducting materials are perfectly diamagnetic in other words, magnetic fields (up to a limiting strength that decreases as the temperature rises toward Tc) cannot penetrate them (the Meissner effect). This is a consequence of the mobile, paired state of the electrons. Indeed, it is the demonstration of the Meissner effect, rather than lack of electrical resistivity, that is usually demanded as evidence of superconductive behavior. One entertaining consequence of the Meissner effect is that small but powerful magnets will float (levitate) above the surface of a flat, level superconductor.30... 

Note that the undoped cuprate is an antiferromagnet and that doping converts it into a superconductor. We have shown above that antiferromagnetic behavior arises from the z = +1 side of the extended Hiickel-Hubbard spectrum in Fig. 4.1. In the ISB theory the superconducting behavior comes from the z = -1 side of Fig. 4.1 just as does the freeon theory of ferromagnetism. 

As with most molecule-based solids, most of the dithiolene complex-based solids are insulators, or, at best, semiconductors, which can hardly be considered as a remarkable property. Therefore, in the following sections we focus on systems exhibiting metal-like or superconducting behavior. 

It is the only series of dithiolene-based compounds (and the only series of molecular metal complex-based compounds) exhibiting superconducting behavior. 

Figure 2.19. Photograph of the Meissner effect for a rare-earth magnet above a sample of YBCO immersed in liquid nitrogen (from http //www.physics.brown.edu/physics/demopages/Demo/em/ demo/5G5050.htm). The onset of strong diamagnetism ( superdiamagnetism, as observed by the repulsion of an external magnetic field) is the most reliable method to determine superconductive behavior.

This model, however, clearly deviates from the experimental data. This is decisive evidence for a perfectly 2D superconducting behavior in the ET compounds. Previous experiments could not definitely distinguish between the two models [191, 195]. 

The FS investigations, however, started only after the discovery of the a-phase family (ET)2MHg(FCN)4 with M = K, NH4, Rb, T1 and F = S or Se. The large number of investigations of these compounds is stimulated by the subtle balance between a low-temperature density-wave state and normal metallic and superconducting behavior which can be tuned comparatively easily in the P—B—T parameter space. The coexistence of closed 2D and open ID FS sheets (see Fig. 2.20) gives the possibility investigating the influence of different dimensionalities within the same material. 

Some chemical aspects such as the effects of comosition and impurities on the manifestation of superconductivity in high-Tc oxides have been described. They are shown to be quite significant in determining superconducting behavior and probably many other physical properties of these materials as well. As the developments of oxide superconductors with higher Tc and better quality continue, it should be essential to take these aspects fully into account. 

Since the initial discovery of higher temperature superconductivity in perovskite copper oxide compounds ( Q, the race for further improving Tc has gone on unabated. The superconducting behavior of La, x Bax Cu 04 y and Y Ba ... 

The superconducting behavior in oxygen defect perovskite oxides is found to depend on the amount and order of oxygen in the structure. In the case of YjBa C y, the highest and sharpest transitions are related to ordering of one-dimensional Cu-O ribbons in the structure which are in turn coupled to a network of adjacent 2-dimensional Cu-O sheets. The isostructural rare earth derivatives of YjBa-jC C y are found to display similar behavior. 

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