Quantum geometry and flat-band superconductivity

Valerio Peri (1), Jonah Herzog-Arbeitman (2), Frank Schindler (2), Zhi-da Song (3), B. Andrei Bernevig (2), Sebastian D. Huber (1)

(1) Institute for Theoretical Physics, ETH Zurich
(2) Department of Physics, Princeton University
(3) International Center for Quantum Materials, Peking University

Flat-band superconductivity demonstrates the importance of band topology and geometry to correlated phases. The geometry of fragile topological and obstructed atomic bands enhances the superfluid weight and hence the superconducting critical temperature. Here, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. Using exact Monte Carlo simulations we prove the validity of our bounds beyond mean-field.