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 the inversion-symmetric Haldane phases of chiral two-dimensional electron gases. We demonstrate that the nontrivial band topology of the Haldane phases enhances intravalley ($\mathbf{Q}=\pm 2{\mathbf{K}}_D$) pair susceptibility relative to intervalley ($\mathbf{Q}=0$) 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 Kekulè superconducting order at low densities. At higher densities, the phase diagram depends on the parity of the Chern number $J$. For even parity, an $s$-wave Kekulè order appears, while for odd parity we find a $\mathbf{Q}=0$ valley triplet chiral $J$ and a valley singlet $s$-wave order at different densities. Our findings are relevant to superconductivity in rhombohedral graphene and Kagome metals.

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• Pair density wave
• Quantum geometry
• Superconductivity