Beyond the Boundaries of Superconductor Modeling

The modeling of unconventional superconductors remains a central challenge in condensed matter physics. Persistent limitations include proximity to spin-density-wave instabilities and unphysical symmetry predictions, leading to deviation from experimental phase diagrams. We address these issues by incorporating Dynamical Mean-Field Theory into fluctuation-exchange (FLEX) diagrammatics via targeted vertex modifications, a strategy that preserves the pairing symmetry captured by FLEX while correcting key deficiencies. Within a computationally scalable framework, we showcase the adjustments required to recover realistic superconducting domes and to chart phase behavior across parameters. The analysis isolates the microscopic sources that shape the dome, clarifying how competing fluctuations and vertex dynamics conspire to produce the observed trends.