Quantum Geometry Induced Kekulé Superconductivity in Haldane phases

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 ($\mathbf{Q}=\pm 2{\mathbf{K}}_{\mathbf{D}}$) pair susceptibility relative to inter-valley ($\mathbf{Q}=0$) 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. Our findings are relevant to superconductivity in rhombohedral graphene and Kagome metals.

8 pages