Limits of Eliashberg theory and bounds for superconducting transition temperatur
Institute of Electrophysics, Ural Branch of the Russian Academy of Sciences, ul. Amundsena 106, Ekaterinburg, 620016, Russian Federation
The discovery of record — breaking values of superconducting transition
temperature Tc in quite a number of hydrides under high pressure was an
impressive demonstration of capabilities of electron—phonon mechanism of
Cooper pairing. This lead to an increased interest to foundations and limitations
of Eliashberg—McMillan theory as the main theory describing superconductivity
in a system of electrons and phonons. Below we shall consider both elementary
basics of this theory and a number of new results derived only recently.
We shall discuss limitations on the value of the coupling constant related to
lattice instability and a phase transition to another phase (CDW, bipolarons).
Within the stable metallic phase the effective pairing constant may acquire
arbitrary values. We consider extensions beyond the traditional adiabatic
approximation. It is shown that Eliasberg—McMillan theory is also
applicable in the strong antiadiabatic limit. The limit of very strong
coupling, being most relevant for the physics of hydrides, is analyzed in details.
We also discuss the bounds for Tc appearing in this limit.