Read-Rezayi fractional Chern insulators in modulated Bernal graphene
Abstract
Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the ℤ3 Read-Rezayi phase in the fractional quantum Hall effect. However, realistic microscopic realizations of this phase in the absence of a magnetic field have remained elusive. We study a model of periodically modulated Bernal bilayer graphene with gate-screened Coulomb interactions. Using the recently developed target-phase optimization method in conjunction with band-projected exact diagonalization, we identify at filling ν=3/5 a region of parameter space whose ground state is consistent with a Read-Rezayi fractional Chern insulator. The partially filled band from which it arises is a part of a two-band complex which mimics geometric aspects of the lowest and first Landau levels, with the ground state at ν=1/2 consistent with the Moore-Read state. Our results suggest that modulated Bernal graphene can realize delicate non-Abelian fractional quantum Hall states at zero magnetic field, while demonstrating target-phase optimization as a practical route to discovering such phases in realistic, high-dimensional microscopic models.
Related
- Weak-coupling theory of half-metals and other fractional metallic phases in biased doped Bernal bilayer graphene
- Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the 𝒩=2 Landau levels of Bernal-stacked bilayer graphene
- Composite Fermion Theory of Fractional Chern Insulators in Rhombohedral Graphene
- Quantum Phase Transitions and Fractional Quantized Anomalous Hall Insulators in Rhombohedral Graphene
- Band mixing and particle-hole asymmetry in moire fractional Chern insulators
BibTeX
@misc{morasoto2026readrezayi,
title = {{Read-Rezayi fractional Chern insulators in modulated Bernal graphene}},
author = {Ruth Mora-Soto and André Grossi Fonseca and Raul Perea-Causin and Hui Liu and Emil J. Bergholtz and Marin Soljačić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31846},
eprint = {2609.31846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Read-Rezayi fractional Chern insulators in modulated Bernal graphene
AU - Ruth Mora-Soto
AU - André Grossi Fonseca
AU - Raul Perea-Causin
AU - Hui Liu
AU - Emil J. Bergholtz
AU - Marin Soljačić
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.31846
UR - https://arxiv.org/abs/2609.31846
AB - Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the ℤ_3 Read-Rezayi phase in the fractional quantum Hall effect. However, realistic microscopic realizations of this phase in the absence of a magnetic field have remained elusive. We study a model of periodically modulated Bernal bilayer graphene with gate-screened Coulomb interactions. Using the recently developed target-phase optimization method in conjunction with band-projected exact diagonalization, we identify at filling ν=3/5 a region of parameter space whose ground state is consistent with a Read-Rezayi fractional Chern insulator. The partially filled band from which it arises is a part of a two-band complex which mimics geometric aspects of the lowest and first Landau levels, with the ground state at ν=1/2 consistent with the Moore-Read state. Our results suggest that modulated Bernal graphene can realize delicate non-Abelian fractional quantum Hall states at zero magnetic field, while demonstrating target-phase optimization as a practical route to discovering such phases in realistic, high-dimensional microscopic models.
ER -