Abstract

Understanding superconductivity in strongly correlated quantum materials remains a central challenge in condensed-matter physics, particularly for systems with partially filled flat bands, where the absence of a Fermi surface precludes intuition based on weak-coupling BCS theory. In this talk, I present an ensemble of exact results on flat-band superconductivity in the strong-coupling limit of local attractive interactions, where the superconducting transition is typically controlled by phase coherence set by the kinetic energy of Cooper pairs, which scales as the inverse of the pair-binding energy. I present a counter-example to this conventional expectation. For electrons hopping on line-graph lattices with strong pairing interactions, Cooper pairs become obstructed: destructive interference frustrates their motion, causing the pair kinetic energy and superfluid stiffness to vanish at leading order. The resulting flat band of compact localized pairs yields an extensively degenerate many-body ground-state manifold. At quarter filling, the system maps onto a quantum dimer model at the Rokhsar-Kivelson point, realizing a d-wave resonating-valence-bond spin liquid with topological ground-state degeneracy and deconfined holon excitations. These results establish a bridge between strongly correlated superconductivity and frustrated magnetism and a disorder-free mechanism for interaction-driven localization, in which strong pairing collapses the kinetic energy of Cooper pairs.

Ref: arXiv:2411.17815