Until 1986, the highest temperature at which superconductivity had been observed was 23.2K in Nb3Ge. There was an issue as to whether BCS theory would impose an upper limit on the critical temperature for the onset of superconductivity. Actually, as remarked before, the exponential factor in (23.24) may be viewed as responsible for the relatively low temperatures of the BCS superconductors. That expression for Tc has in fact a mathematical upper limit, of the order of the Debye temperature, which is typically about a few hundred Kelvin. This, however, would correspond to an infinite value of the product ƛN(EF) of coupling parameter and Fermi level density-of-states. The mathematical upper bound, consequently, is way above the temperatures corresponding to realistic physical values of parameters. In 1986, La2–xx BaxCuO4 and La2–x SrxCuO4 (LSCO) where shown to present a superconducting phase at temperatures up to about 40K. Soon after, Y Ba2Cu3O6+x (YBCO) was shown to have a superconducting phase up to 92K. These were the first members of the cuprate family, which contains materials such as HgBa2Ca2Cu3O8+x, which exhibits a superconducting phase up to a temperature of the order of 130K without pressure and of about 160K under high pressure. Many indications suggest that the mechanism leading to superconductivity in cuprates is not the phonon-mediated BCS mechanism. There is general consensus on this point. Nevertheless, there is so far no agreement about the specific mechanism leading to the formation of Cooper pairs in cuprates, despite the many proposals that have been made. In this chapter, we keep mostly in the region where consensus has been reached, except for Section 24.4, which contains our own contribution to the subject.

Crystal Structure, CuO2 Planes and Phase Diagram

A common feature of all materials belonging to the cuprates family is the presence of CuO2 planes, consisting in a square lattice, which, before doping, contains Cu++ ions on the sites and O−− ions on the links. The latter has a 2p6 electronic configuration, whereas the former is in a 3d9 configuration. The oxygen ions are in a noble gas configuration, while the copper ions have an unpaired electron, which creates a localized magnetic moment at each site.