Quantum Geometric Unconventional Superconductivity

Coulomb repulsion can, counterintuitively, mediate Cooper pairing via the Kohn-Luttinger mechanism. However, it is commonly believed that observability of the effect requires special circumstances -- e.g., vicinity of the Fermi level to van Hove singularities, significant lattice-induced band distortions, or non-trivial Fermi surface topologies. In this talk, I will show that quantum geometric properties of the constituent electrons can dramatically promote pairing from repulsion via dependence of screening on the quantum metric. Exploring quantum-geometry-enhanced superconductivity in two microscopic models with tunable quantum geometry, I will highlight the crucial roles of quantum metric anisotropy and inhomogeneity. The analysis provides an experimentally accessible figure of merit for the importance of quantum geometry to inducing unconventional superconductivity, indicating its relevance to graphene multilayers. Time permitting, I will discuss a subtle unresolved mystery in bilayer graphene which fits nicely into this paradigm.