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

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.