High temperature superconductivity?

The fundamental mystery of the high temperature superconductivity seems very deep. Here I will try to explain an important aspect of it, in a way that is, hopefully, understandable to any one.

The superconductivity

Let us think of the superconductivity, first, before thinking of the high-temperature superconductivity. It is a well-known fact that many heroes of the modern physics (Einstein, Feynmann, et al.) have tried to explain the superconductivity, and did not succeed. What was so difficult?

Normal electron and superconducting electrons

The triumph of the BCS (Bardeen-Cooper-Schrieffer) theory is based on the distinction between these two: normal electron and superconducting electrons. At high temperature, normal electrons conduct the electricity. For instance, this is how the electricity conducts in Copper wires. If a metal is cooled down to very low temperature, it is often found to superconduct—the resistivity drops to zero, suddently (perfect conductor), and it expels any magnatic field (perfect diamagnet). According to the BCS theory, which is the theory of the superconductors that we have so far, the superconductivity occurs due to pairs of electrons (Cooper pairs).