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 MoTe2. 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−i f hole superconductors and find additional p± i p and f+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− i p electron and f−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.
Related
- Flat Chern bands and correlated states in spiral magnet
- Vortexable Chern Bands Sit Exactly on the Topological Floor of Flat-Band Superfluid Stiffness
- Spontaneous Chirality and Collective Chern Bands in a Dipole-Conserving Bose System
- Composite fermions in ideal Chern bands
- Anyon Chern bands of opposite sign and reversed drift
BibTeX
@misc{fonseca2026zoology,
title = {{Zoology of chiral superconductors in Chern bands}},
author = {André Grossi Fonseca and Aidan Reddy and Ahmed Abouelkomsan and Liang Fu and Marin Soljačić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31839},
eprint = {2609.31839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31839},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zoology of chiral superconductors in Chern bands
AU - André Grossi Fonseca
AU - Aidan Reddy
AU - Ahmed Abouelkomsan
AU - Liang Fu
AU - Marin Soljačić
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31839
UR - https://arxiv.org/abs/2609.31839
AB - 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−i f hole superconductors and find additional p± i p and f+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− i p electron and f−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.
ER -