Quantum Geometric Kohn-Luttinger Superconductivity

TL;DR

This paper shows that quantum geometric properties of electrons can significantly enhance superconductivity mediated by Coulomb repulsion, especially in materials like graphene multilayers, by influencing screening through the quantum metric.

Contribution

It introduces the concept that quantum geometry, particularly the quantum metric, can promote Cooper pairing from repulsive interactions, expanding understanding of unconventional superconductivity.

Findings

Quantum metric anisotropy and inhomogeneity enhance pairing.

Quantum geometry effects are significant in graphene multilayers.

Screening dependence on quantum metric promotes superconductivity.

Abstract

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. Here we establish that quantum geometric properties of the constituent electrons can dramatically promote pairing from repulsion via dependence of screening on the quantum metric. We demonstrate quantum-geometry-enhanced superconductivity in two microscopic models with tunable quantum geometry, highlighting the crucial roles of quantum metric anisotropy and inhomogeneity. Our analysis provides an experimentally accessible figure of merit for the importance of quantum geometry to inducing unconventional superconductivity, indicating its relevance to graphene multilayers.