Eliashberg theory of superconductivity

Synopsis

Eliashberg theory is a theoretical model of superconductivity based on electron-phonon interactions. Phonons correspond to vibrations of the atoms in a crystal lattice. Electrons exchange energy with these phonons, which causes the atoms in the lattice to be displaced from their equilibrium positions. The theory is based on the principle that the effective electron-electron attraction is retarded in time due to the dynamical nature of the electron-phonon interaction. This talk focuses on distinguishing physical properties between weak-coupling Eliashberg theory and Bardeen-Cooper-Schrieffer (BCS) theory.

In this seminar, I will explain the gap ratio, which is the ratio of the zero-temperature gap function to the critical temperature. Both zero-temperature gap function and the critical temperature (the temperature at which superconductivity will be removed) are two important energy scales in superconductivity. I will also talk about the specific heat (the amount of energy that is needed for increasing the temperature) and the electrical conductivity (the response to an external electric field). Despite the universality in both theories for the gap ratio and normalized specific-heat jump, the electrical conductivity does not have a universal value. This suggests that the presence of a dynamical electron-phonon interaction in a material can be established by determining its electrical response.