Quantum-Geometry-Induced Superconductivity near a Fractional Chern Insulator
arXiv:2606.21166
The paper analytically studies how quantum‑geometric effects in a partially filled Chern band can generate superconductivity adjacent to a fractional Chern insulator, using a coupled‑wire and bosonization approach.
Abstract
Recent moiré experiments and numerical studies of interacting Chern bands have revealed fractional Chern insulators, charge-density-wave order, and superconductivity as proximate correlation-driven phases in topological systems. How these phases compete or intertwine, and how quantum geometry shapes their interplay, remain open questions. Here we present an analytic study of competing correlation-driven phases in a partially filled Chern band using a coupled-wire construction and bosonization. The key ingredient is the coexistence of interaction channels that favor, respectively, a fractional Chern insulator (FCI) and a closely related anti-FCI (aFCI) state. The aFCI channel is specific to lattice Chern bands and is enhanced by the quantum geometry of the underlying band structure. We show that when both FCI and aFCI scattering channels are present, their interplay generates an effective coupling that drives a superconducting instability near the FCI phase. The same mechanism can also favor a charge-density-wave phase, depending on microscopic parameters. Using a perturbative renormalization-group analysis, we obtain the phase diagram and identify a superconducting regime adjacent to the FCI phase. We further estimate the superconducting transition temperature and show that it is enhanced by quantum geometry. Our results establish quantum geometry as an organizing principle for the interplay among FCI, aFCI, and superconducting correlations.
28 pages, 6 figures