Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys under pressure

摘要

In a short review-article we first discuss the results, which are mainlydevoted to the generalizations of the famous Kohn-Luttinger mechanism ofsuperconductivity in purely repulsive fermion systems at low electrondensities. In the context of repulsive-U Hubbard model and Shubin-Vonsovskymodel we consider briefly the superconducting phase diagrams and the symmetriesof the order parameter in novel strongly correlated electron systems includingidealized monolayer and bilayer graphene. We stress that purely repulsivefermion systems are mainly the subject of unconventional low-temperaturesuperconductivity. To get the high temperature superconductivity in cuprates(with T_C of the order of 100 K) we should proceed to the t-J model with theVan der Waals interaction potential and the competition between short-rangerepulsion and long-range attraction. Finally we stress that to describesuperconductivity in metallic hydrogen alloys under pressure (with T_C of theorder of 200 K) it is reasonable to reexamine more conventional mechanismsconnected with electron-phonon interaction. These mechanisms arise in theattractive-U Hubbard model with static onsite or intersite attractive potentialor in more realistic theories (which include retardation effects) such asMigdal-Eliashberg strong coupling theory or even Fermi-Bose mixture theory ofRanninger et al., and its generalizations.