The Condition for the Onset of High Temperature Superconductivity

In this work the long-wave limit of electron-electron interaction arising from the exchange of virtual phonons in an approximation close to "jelly" model is considered. It is shown that the interaction through the exchange of virtual phonons is actually not screened in contrast to the Coulomb one; this just leads to instability relative to the formation of pairs near the Fermi surface. The consequences of this approach are examined with respect to high-temperature superconducting materials that have recently been synthesized. An approximate relationship connecting sound and Fermi velocities for these materials is obtained.