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arXiv · 2609.31846

Read-Rezayi fractional Chern insulators in modulated Bernal graphene

Ruth Mora-Soto·André Grossi Fonseca·Raul Perea-Causin·Hui Liu·Emil J. Bergholtz·Marin Soljačić
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Abstract

Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the $\mathbb{Z}_3$ 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.

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Ruth Mora-Soto, André Grossi Fonseca, Raul Perea-Causin, Hui Liu, Emil J. Bergholtz, Marin Soljačić. 2026-09-25. Read-Rezayi fractional Chern insulators in modulated Bernal graphene. https://arxiv.org/abs/2609.31846

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