Microscopic Theory of the Tolmachev-Morel-Anderson Pseudopotential

The Tolmachev-Morel-Anderson pseudopotential is a widely used element in the conventional superconductivity theory, but a controllable first principle approach to this quantity remains absent. We re-examined the interplay between the electron-phonon and Coulomb interactions in the superconductivity problem by leveraging modern quantum field theoretical frameworks, and established a microscopic theory for the pseudopotential. Based on the theory we developed a controllable first principle diagrammatic Monte Carlo technique to compute this quantity for small to moderate values of r_s in a uniform electron gas with weak phonon coupling. The results showed the applicability of our approach from conventional cases to the realm of ultralow-temperature superconductors.