Zoology of chiral superconductors in Chern bands

Abstract

Evidence for chiral superconductivity has recently been observed in several van der Waals systems including rhombohedral multilayer graphene and twisted bilayer MoTe$_2$. In the latter, superconductivity emerges at carrier densities near a fractional Chern insulator. This raises the question of what kinds of superconductors may emerge in a system of electrons in a topological band with strong repulsive interactions. Here, we adapt the target-phase optimization method to search for chiral superconductors in a minimal model of interacting electrons in a Chern band. We construct a differentiable loss function for superconductors from the sign oscillation of the pair-binding energy and combine gradient-based optimization with a rigorous screening procedure to identify and characterize superconductors. Applying this framework within exact diagonalization to spinless electrons in periodically modulated Landau levels with screened Coulomb interactions, we uncover a broad family of chiral superconducting phases. At filling $ν=2/3$, we recover the previously identified $f-\mathrm{i} f$ hole superconductors and find additional $p\pm \mathrm{i} p$ and $f+\mathrm{i} f$ superconductors of both electrons and holes, occurring near and far from the limit of ideal quantum geometry. At $ν=1/2$, we identify $p- \mathrm{i} p$ electron and $f-\mathrm{i} f$ hole superconductors and find, for the first time, a direct transition between chiral superconductors and composite Fermi liquids. Our results reveal that chiral superconductivity in Chern bands comprises a diverse landscape of competing pairing instabilities and establish target-phase optimization as a general strategy for searching for quantum phases in complex interacting systems.