Role of Thermal Phonons in High-Temperature Superconductivity

Abstract

With Éliashberg's equations for the two temperature Green's functions of a superconductor, the effect of real phonons on the transition temperature $T_c$ is discussed. The equation derived for $\frac{T_c}{T_{c0\mathrm{}}}$ describes a temperature-depdendent pair-breaking mechanism that depends on both the real and the imaginary part of the electron-phonon self-energy ($T_{c0\mathrm{}}=\mathrm{transition}\mathrm{temperature}\mathrm{in}\mathrm{the}\mathrm{absence}\mathrm{of}\mathrm{real}\mathrm{phonons}$).