Abstract

The richness of strongly correlated quantum matter (SCQM) emerges from an evenly matched tug-of-war between quantities that cannot be minimized at once — kinetic energy and local interaction energy, much as position and momentum cannot be known at once. A long-standing challenge is to describe high-temperature superconductivity in SCQM in a way that holds up both in the weak-coupling limit, where Bardeen–Cooper–Schrieffer (BCS) theory is grounded, and in the strong-coupling limit, where heavy-fermion pairing mechanisms are rooted.
Topological flat bands offer a new opening to this enduring problem. These bands host a macroscopic degeneracy of compact localized states, which are molecular orbitals whose delocalization is frustrated by the topology of the graph on which the electrons can hop. Such extensive degeneracies imply an infinite susceptibility to any non-commuting perturbations, exemplified by the menagerie of exotic quantum phases that have been recently discovered in moiré heterostructures.
In this talk, I will first demonstrate the construction of an infinite family of flat-band models protected by graph topology[1], exploring their broad implications across quantum information, quantum glasses with no classical analog, and topologically protected computation without anyons. I will then address the problem of flat band superconductivity, where the absence of a Fermi surface precludes intuition based on BCS theory, from the strong-coupling limit[2]. This approach uncovers new strong-coupling degrees of freedom that have no weak-coupling analog and an unexpected bridge between superconductivity and frustrated magnetism. Specifically, I will map strong-coupling superconductivity onto a quantum dimer model, whose ground state is exactly solvable - a resonance of exponentially many configurations of covalent sigma-bonds. Finally, I will show that the many-body eigenspectrum of this dimer model features non-ergodic athermal eigenstates, localized in Hilbert space by the same topological frustration that yields single-particle flat bands.
Addressing the physics of flat bands through the mathematics of graph topology and the chemistry of covalent bonding and its topological obstruction allows us a unique opportunity to unify the competing perspectives of strongly correlated superconductivity either mediated by delocalized spin-fluctuations that are often tied to quantum criticality or driven by local moments which are Kondo-screened to become part of the superconducting condensate itself. This program of unifying strongly correlated superconductivity will continue to draw intuition from, and in turn cross-fertilize, the fields of frustrated magnetism and disorder-free localization.
[1] Hazra, arxiv.org/abs/2607.22831 (2026)
[2] Hazra, Verma, Schmalian, scipost.org/submissions/2411.17815v4 (2026)