In review, we discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low density. We construct phase diagrams of these systems and find the areas of superconducting state in free space, as well as in the lattice in the framework of the Fermi-gas model with hard-core repulsion, Hubbard model, Shubin—Vonsovsky model, and t—J model. We demonstrate that the critical superconducting temperature can be strongly increased in a spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn—Luttinger mechanism or its generalizations and explains or predicts anomalous p-, d- and f-wave pairing in various materials, such as high-temperature superconductors, idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid ³He, spin-polarized solutions ³He in ⁴He, ultracold quantum gases in magnetic traps and in the optical lattices.

Keywords: anomalous superconductivity, Kohn—Luttinger mechanism, superfluidity, repulsive Fermi gas, Hubbard and t—J model, Shubin—Vonsovsky model, graphene monolayer, graphene bilayer PACS: 67.85.−d, 74.20.−z, 74.20.Mn, 74.20.Rp, 74.25.Dw, 74.78.Fk, 81.05.ue (all) DOI: 10.3367/UFNe.0185.201508a.0785 URL: https://ufn.ru/en/articles/2015/8/a/ 000364717300001 2-s2.0-84947767252 2015PhyU...58..733K Citation: Kagan M Yu, Mitskan V A, Korovushkin M M "Anomalous superconductivity and superfluidity in repulsive fermion systems" Phys. Usp. 58 733–761 (2015) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 15th, May 2015, accepted: 9th, June 2015 Оригинал: Каган М Ю, Мицкан В А, Коровушкин М М «Аномальная сверхпроводимость и сверхтекучесть в фермионных системах с отталкиванием» УФН 185 785–815 (2015); DOI: 10.3367/UFNr.0185.201508a.0785