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Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands

Hui Liu1,*, Zhao Liu2,3,†, and Emil J. Bergholtz1,‡

  • 1Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
  • 2Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310058, China
  • 3Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, School of Physics, Zhejiang University, Hangzhou 310027, China

  • *Contact author: hui.liu@fysik.su.se
  • †Contact author: zhaol@zju.edu.cn
  • ‡Contact author: emil.bergholtz@fysik.su.se
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Phys. Rev. Lett. 135, 106604 – Published 4 September, 2025

DOI: https://doi.org/10.1103/43nq-ntqm

Abstract

Breakthrough experiments have recently realized fractional Chern insulators (FCIs) in moiré materials. However, all states observed are Abelian; the possible existence of more exotic non-Abelian FCIs remains controversial both experimentally and theoretically. Here, we investigate the competition between charge density wave (CDW) order, gapless composite fermion liquid (CFL), and non-Abelian Moore-Read states at half filling of a moiré band. Although ground-state (quasi)degeneracies and spectral flow are not sufficient for distinguishing between charge order and Moore-Read states, we find evidence using entanglement spectroscopy that both these states of matter can be realized with Coulomb interactions. By further analyzing the graviton excitations of Moore-Read states, we unveil that the ground states exhibit a mixed behavior of Pfaffian and anti-Pfaffian, despite the weak breaking of particle-hole symmetry. In a double twisted bilayer graphene model, transitions between these phases can be driven by the coupling strength between the layers: at weak coupling there is a CFL phase and at strong coupling a CDW order emerges. Remarkably, however, there is compelling evidence for a non-Abelian Moore-Read FCI phase at intermediate coupling.

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Phys. Rev. Lett. 135, 106604– Published 4 September, 2025
  • Received 22 May 2024
  • Revised 21 July 2025
  • Accepted 8 August 2025
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