High-T\(_c\) and Low-T\(_c\) Superconductivity in Electron Systems With Repulsion

We demonstrate the instability of the normal state of purely repulsive fermionic systems towards the transition to the Kohn-Luttinger superconducting state. We construct the superconducting phase diagrams of these systems in the framework of the Hubbard and Shubin-Vonsovsky models on the square and hexagonal lattices. We show that an account for the long-range Coulomb interactions, as well as the Kohn- Luttinger renormalizations lead to an increase in the critical superconducting temperatures in various materials, such as high-temperature superconductors, idealized monolayer and bilayer of doped graphene. Additionally, we discuss the role of the structural disorder and the nonmagnetic impurities in superconducting properties of real graphene systems.