Role of Thermal Phonons in High-Temperature Superconductivity

With \'Eliashberg'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 $\frac{{T}_{c}}{{T}_{c0}}$ describes a temperature-depdendent pair-breaking mechanism that depends on both the real and the imaginary part of the electron-phonon self-energy (${T}_{c0}=\mathrm{transition}\mathrm{temperature}\mathrm{in}\mathrm{the}\mathrm{absence}\mathrm{of}\mathrm{real}\mathrm{phonons}$).

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