Condensed Matter Seminar: Collective modes and superfluid properties of superconductors with Coulomb repulsion: a field theory approach

Coulomb repulsion exists in all superconductors and is especially strong in unconventional ones, yet its effect on the properties of the superconducting state remains poorly understood. The standard theoretical tool, the Morel-Anderson pseudopotential µ*, reduces repulsion to an effective attractive interaction that correctly predicts the critical temperature. However, µ* is only rigorously justified in a limit far from real materials, in the weak coupling limit, and it provides no framework for the collective modes, superfluid stiffness, or pairing fluctuations of the resulting superconductor. We present a field theory that incorporates bare Coulomb repulsion directly into the fluctuation physics, without invoking µ*. Our approach reveals two collective modes generated purely by repulsion, with no counterpart in any attractive theory, that produce a large and non-trivial dependence of experimentally accessible properties, superfluid stiffness, coherence length, compressibility, and pairing susceptibility, on the strength of Coulomb repulsion, even between systems with identical critical temperatures. We confirm these predictions using a quantum Monte Carlo scheme that overcomes the sign problem introduced by repulsion using holomorphic flow into the complex plane. Our theory makes the fingerprints of Coulomb repulsion on the superconducting state readily accessible and shows that they grow in importance as the coupling strength increases toward values relevant for real materials.