Microscopic theory of superconductivity near a Lifshitz transition

Observation of robust superconductivity in some of the iron based superconductors in the vicinity of a Lifshitz point has attracted many theoretical and experimental studies. The majority of these studies have been phenomenological. Here we discuss a microscopic treatment of the pairing mechanism for a bilayer Hubbard model, which goes through a Lifshitz transition. We study pairing driven by spin-fluctuations by solving the strong coupling Eliashberg equations and make a systematic comparison of the results with non-perturbative dynamical cluster quantum Monte Carlo calculations. Our findings are quite general and we will discuss their application to some of the iron based superconductors.