The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene

TL;DR

This review discusses the Kohn-Luttinger mechanism as a nonphonon route to superconductivity across various materials, highlighting phase diagrams, anomalous pairing, and potential for high transition temperatures even at low electron densities.

Contribution

It provides a comprehensive overview of the Kohn-Luttinger theory's application to diverse systems, including graphene and topological superconductors, emphasizing novel pairing symmetries and elevated $T_c$ possibilities.

Findings

Superconductivity can arise from repulsive interactions via Kohn-Luttinger mechanism.

Anomalous $s$-, $p$-, and $d$-wave pairings are possible in various systems.

High $T_c$ superconductivity may occur even at low electron densities.

Abstract

We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous $s$-, $p$-, and $d$-wave pairing. The possibility of a strong increase in the superconducting transition temperature $T_c$ even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-$T_c$ superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid $^3$He-A, doped graphene, and topological superconductors.