In my talk, I review recent and not so recent works aiming to understand whether a nominally repulsive Coulomb interaction can by itself give rise to a superconductivity. I discuss a generic scenario of the pairing by electron-electron interaction, put forward by Kohn and Luttinger back in 1965, and modern studies of the electronic mechanisms of superconductivity in the lattice systems, which model cuprates, Fe-based superconductors, and even doped graphene. I show that the pairing in all three classes of materials can be viewed as a lattice version of Kohn-Luttinger physics, despite that the pairing symmetries are different. I discuss under what condition the pairing occurs and rationalize the need to do renormalization-group studies. I also discuss most recent work on the interplay between the true superconductivity and the pseudogap behavior, in which the pairing gap is present but superconducting order is destroyed by fluctuations.
Host: Arun Paramekanti