# Quantum Geometry Induced Kekul\'{e} Superconductivity in Haldane phases

## TL;DR

This paper explores how the nontrivial topology of Haldane phases in chiral 2D electron gases promotes Kekulé superconductivity mediated by phonons, with implications for graphene and Kagome metals.

## Contribution

It reveals that the band topology enhances intra-valley pairing, leading to a novel Kekulé superconducting order in Haldane phases.

## Key findings

- Intra-valley pair susceptibility is enhanced by nontrivial band topology.
- Lattice-scale pair-density wave order is favored over inter-valley pairing.
- Chiral Kekulé superconductivity can be mediated by acoustic phonons.

## Abstract

Chiral two-dimensional electron gases, which capture the electronic properties of graphene and rhombohedral graphene systems, exhibit singular momentum-space vortices and are susceptible to interaction-induced topological Haldane phases. Here, we investigate pairing interactions in these inversion-symmetric Haldane phases of chiral two-dimensional electron gases. We demonstrate that the nontrivial band topology of the Haldane phases enhances intra-valley (${\bf Q} = \pm 2 {\bf K_D}$) pair susceptibility relative to inter-valley (${\bf Q} = 0$) pair susceptibility, favoring the emergence of a lattice-scale pair-density wave order. When longitudinal acoustic phonons mediate the pairing interaction, the system supports a chiral Kekul\`{e} superconducting order. Our findings are relevant to superconductivity in rhombohedral graphene and Kagome metals.