Superconductivity in two-band non-adiabatic systems

This article is a review o over theory of superconductivity, which is constructed for systems with two overlapping energy bands at the Fermi surface and with arbitrary charge carrier density.There is taken into account all possible kinds of electron pairing within each band and of electron pairing from different bands. A bell-shape dependence of superconducting-transition temperature $T_c$ on the electron density, and have demonstrated a possible onset of HTSC. The absolute a...

The main stages of development of the theory of superconductivity in systems with overlapping energy bands are formulated. The main references on the classical papers of the author of this theory, Prof. Moskalenko V.A., and his coworkers are listed. The list also includes papers related to high - temperature superconductivity. Some peculiarities of the two - band model, which lead to qualitatively new results in comparison to the usual one - band model, are enumerated. We als...

High-$T_c$ superconductors are usually described as strongly correlated electronic systems. This feature deeply affects the one-particle and two-particle properties of the system. In particular, a large incoherent background developes on the top of a narrow quasi-particle peak in the one-electron spectral function. We schematize this structure with a simple phenomenological form. The corresponding Green's function is employed to calculate the charge response of the system tak...

The possible strong electron-phonon coupling and the pairing within the full width of the electron band and not only in a narrow sheet near the Fermi surface are taken into account. It is found that the effect of pairing of electrons belonging to different bands is crucial to the appearance of high Tc in some two-band materials. The existence of another set of the two-band high temperature materials with transition temperature Tc, not yielding Tc in cuprates, is predicted.

In this chapter we review the essentials of conventional electron-phonon superconductivity, as provided through the Migdal-Eliashberg formalism. Signatures of the electron-phonon interaction, as they appear in conventional superconductors, are described in detail. An appendix briefly describes more recent attempts to understand the electron-phonon interaction for all coupling strengths.

High-$T_c$ superconductors are characterized by very low carrier densities. This feature leads to two fundamental consequences: on one hand the Fermi energies are correspondingly small and they can be of the same order of phonon frequencies. In such a situation nonadiabatic corrections arising from the breakdown of Migdal's theorem can not be longer neglected. In addition, small carrier densities imply poor screening and correlation effects have to be taken into account. We p...

We solve the anisotropic, full-bandwidth and non-adiabatic Eliashberg equations for phonon-mediated superconductivity by fully including the first vertex correction in the electronic self-energy. The non-adiabatic equations are solved numerically here without further approximations, for a one-band model system. We compare the results to those that we obtain by adiabatic full-bandwidth, as well as Fermi-surface restricted Eliashberg-theory calculations. We find that non-adiaba...

The theory of thermodynamic properties of two-band superconductor with reduced density charge carriers is developed on the base of phonon superconducting mechanism with strong electron-phonon interaction. This theory is adapted to describe the behavior of critical temperature Tc, energy gaps Delta1, Delta2, and the relative jump of electron specific heat (Cs - Cn)/Cn in the point T = Tc along with the variation of charge carrier density in the compound MgB2 when substitutiona...

Within a minimal model for the iron-based superconductors in which itinerant electrons interact with a band of local moments, we derive a a general conclusion for multi-band superconductivity. In a multi-band superconductor, due to the Adler theorem, the inter-band scattering dominates the intra-band scattering at the long wave length limit as long as both interactions are induced by Goldstone boson (which is magnon in our case) and the transfered momentum is nonzero. Such ki...

The publication of a revised edition of a monograph devoted to the two-band theory of superconductivity provides us the opportunity of a short comment on two classical papers, published independently some 50 years ago, where the generalization of the BCS theory for metals with overlapping energy bands at the Fermi level has been proposed. The article includes Moskalenko's recollections on some aspects of scientific life in the Soviet Union, in the '50s.