What Do We Know About the Mechanism of Superconduc9vity at “Intermediate Coupling?”

Abstract

Because a Fermi liquid is unstable to superconductivity in the presence of an arbitrarily weak effective attractive interaction in any Cooper channel, most theories of superconductivity effectively involve extrapolation from a weak coupling limit. To obtained theoretically well controlled results at intermediate coupling, one must either rely on (painfully time consuming) numerics or identify special model problems for which exact results can be extracted in one way or another, or be extremely clever. I will discuss some results that my collaborators and I have obtained - recently and less recently - on various aspects of this class of problems using all the tools available to us (i.e. without being clever). While these studies are motivated by the physics of various real materials - such as the cuprates, A3C60, magical graphene, and possibly even H3S - what I will discuss is the properties of simple model Hamiltonians.