- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation

    Field-tuned and zero-field fractional Chern insulators in twisted bilayer graphene

    Daniel E. Parker1,2, Patrick Ledwith1, Eslam Khalaf1, Tomohiro Soejima3,4,5, Johannes Hauschild3, Yonglong Xie1,6,7, Andrew Pierce1, Michael P. Zaletel3,8, Amir Yacoby1,9 et al.

    Ashvin Vishwanath1

    • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
    • 2Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
    • 3Department of Physics, University of California, Berkeley, California 94720, USA
    • 4Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
    • 5Center for Quantum Phenomena, Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA
    • 6Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
    • 7Department of Physics and Astronomy, Smalley Curl Institute, Rice Advanced Materials Institute, Rice University, Houston, Texas 77005, USA
    • 8Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
    • 9John A. Paulson School of Applied Sciences and Engineering, Harvard University, Cambridge, Massachusetts 02138, USA

    PDF

    Phys. Rev. B 114, 295104 – Published 5 November, 2026

    DOI: https://doi.org/10.1103/gmtx-h1gs

    Abstract

    In contrast to the fractional quantum Hall (FQH) effect, where electron density fixes the applied magnetic field, fractional Chern insulators (FCIs) can realize FQH states in comparatively weak or even zero magnetic fields. Previous theoretical work highlighted magic-angle graphene as a promising FCI platform, satisfying the twin requirements of flat Chern ±1 bands and lowest-Landau-level-like quantum geometry. Indeed, recent experiments have demonstrated FCIs in magic angle graphene with weak magnetic fields. Here we conduct a detailed theoretical study of the most prominent FCI state observed, and we clarify the role of the magnetic field in stabilizing this state. We introduce two new technical tools: first, we generalize the notion of ideal quantum geometry to Hofstadter minibands, and second, we extend the Hartree-Fock theory of magic-angle graphene to finite field, to account for the interaction-generated bandwidth. We show that magnetic field both dramatically reduces the effective bandwidth and improves the quantum geometry for hosting FCIs. Using density matrix renormalization group simulations of a microscopic model of magic-angle graphene, we establish the regime of bandwidth and quantum geometry indicators where FCIs are stabilized. Further characterizing the finite-field bands by the same quantities, we show how a zero-field charge density wave state gives way to an FCI state at a magnetic flux consistent with experiment. We also speculate on the other FCIs seen in the same experiments, including anomalous incompressible states and even-denominator fractions, which may host non-Abelian states. Finally, we propose a range of experimental parameters where FCIs should appear at zero magnetic field, when bandwidth is the limiting factor.

    View figure in article

    Physics Subject Headings (PhySH)

    Authorization Required

    We need you to provide your credentials before accessing this content.

    Other Options

    References (Subscription Required)

    Outline

    Information

    Phys. Rev. B 114, 295104– Published 5 November, 2026
    • Received 16 May 2022
    • Revised 6 November 2025
    • Accepted 3 June 2026
    Article part of CHORUS
    Accepted manuscript will be available starting 5 November, 2027.
    Crossmark - Check for updates button

    ©2026 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation