Superconducting weak coupling

All the high Tc superconductors discovered so far, with one exception, contain weakly coupled copper oxide, Cu02, planes. The highest critical temperatures are found for cuprates containing a Group 2 metal (Ca, Ba, Sr) and a heavy metal such as Tl, Bi, or Hg. The structures of all the cuprate superconductors are based on, or related to, the perovskite structure. The one report (in 2000) of a non-cuprate high T superconductor is of surface superconductivity in Na WOs. The structure of NUxWOs is also based on the perovskite structure. 

However, in the preceding two decades, there have been many experimental discoveries, beside high-Tc superconductivity, evidencing that we do not have yet the proper theoretical skills and tools to deal well with strongly correlated electron systems. For instance, heavy-fermions, fractional quantum Hall effect, ladder materials, and very specially high-Tc superconductivity seem not accessible from the weak coupling limit. 

We start from a two-dimensional free electron gas. The Fermi surface in this model is circular and the band width is infinite. Superconducting properties are described in a Fermi surface restricted approach, so that the weak coupling selfconsistency equation reads... 

Rosseinsky et al. also suggested a simple reason for the large increase in transition temperature when Rb is substituted for K. The most elementary, widely understood theory of superconductivity, the weak-coupling Bardeen-Cooper-Schrieffer (BCS) model,[Bat57] predicts a simple connection between transition temperature Tc, phonon energy w, electron-phonon coupling strength V, and the density of electron states at the Fermi surface N EfI... 

We speculated previously that superconductivity in KjCso and Rb3Ceo resulted from electron pairing mediated by high-frequency intramolecular phonons of the Qo molecule, with the change in between KaCeo and RbaCso explained by a change of the density of states at the Fermi level by about 10%. In this weak-coupling BCS model, the variation of is given by... 

A Josephson junction consists of two closely spaced superconductors separated by a weak connection (Figure 4.6.1). This connection may be provided by an insulator, a normal metal, a semiconductor, a weakened superconductor, or some other material that weakly couples the two superconductors. The two superconducting regions may be characterized by quantum mechanical wave functions and 2 respectively. Normally a much more complicated description would be necessary because... 

The Josephson effect is the phenomenon in which two superconducting materials weakly coupled through a non-superconducting interface show a sharp increase in conductance of current flowing from one of the superconductors to the other if radiation of a suitable frequency is applied to the interface. The relation between the voltage difference between the two superconductors Uj and the frequency / of the applied radiation for which there is an increase in current is given by... 

As the mechanism of superconductivity in these doped fullerites was not clear, the greatest attention was directed to the standard mechanism of superconductivity. The conventional theory is based on the electron-phonon interaction and generalized in the Eliashberg equations which include the Bardeen, Cooper and Schrieffer (BCS) equation as a weak-coupling limit [78]. For real superconductors the ratio for the weak-coupling limit is close to the value of 3.52, and for stronger coupling materials it increases up to about 5.1... 

It is now generally agreed, however, that the observed increase in results from suppression of charge density wave formation rather than some exotic quasi-two-dimensional mechanism. However, the effect of the two-dimensional anisotropy of the material is of considerable interest. It has been found that the critical field behavior is in broad agreement with theoretical predictions based on a model of a layered compound containing two-dimensional superconducting layers weakly coupled via Josephson tunneling. ... 

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