The Hofstadter Butterfly in Magic-Angle Bilayer Graphene Reveals New Strongly Interacting Phases

Hofstadter butterfly in bilayer graphene

Graphene has repeatedly astonished the scientific community since its isolation in 2004, but magic-angle twisted bilayer graphene (MATBG) has elevated this wonder material into a rich platform for exploring exotic quantum phases. By stacking two graphene layers at a twist angle of about 1.1°, electrons slow down and give rise to highly correlated states, including superconductivity, ferromagnetism, and topological orders.

A new study, published in Nature Physics, reports that MATBG under a magnetic field exhibits two distinct strongly interacting topological phases: symmetry-broken Chern insulators (SBCIs) and fractional quantum Hall (FQH) states. These findings, uncovered by researchers from the University of Washington, Florida State University, and collaborators, highlight the interplay between topology, correlations, and moiré superlattices (Phys.org source).

The Hofstadter Butterfly Emerges

When a magnetic field is applied to MATBG, its flat energy bands form a fractal-like pattern known as the Hofstadter butterfly, first predicted by Douglass Hofstadter in 1976. This recursive spectrum arises because the moiré superlattice imposes a periodic potential on electrons, making their trajectories sensitive to the magnetic flux through each unit cell.

In ultraclean MATBG devices measured at millikelvin temperatures, researchers observed cascades of Hofstadter states that fit within this framework but revealed features that no existing theory could fully explain. The breakthrough came when new theoretical tools extending the Hofstadter model to include strong interactions were applied, finally matching experimental data.

Two Interacting Topological Phases

The experiments revealed two remarkable phenomena:

  • Symmetry-broken Chern insulators (SBCIs): Unusual topological states where the moiré unit cell spontaneously enlarges. Unlike earlier reports of sporadic SBCIs, the researchers found a cascade sequence with systematically evolving Chern numbers.
  • Fractional quantum Hall (FQH) states: Emergent under strong magnetic fields, these states followed a Jain-sequence hierarchy predicted by composite fermion theory. Intriguingly, they disappeared above ~10 T, highlighting the unique length scales of moiré systems.

Together, these results suggest that FQH states in MATBG are unconventional and may be better understood as fractional Chern insulators induced by magnetic fields.

Why This Matters

The discovery not only deepens our understanding of MATBG but also demonstrates the richness of correlated quantum matter in moiré materials. The unusual quantum geometry of these states, with finite bandwidth and non-uniform properties, offers fertile ground for exploring new topological phases that could underpin future quantum computing and low-power electronics.

“Our Hartree–Fock band analysis shows that these fractional states arise out of strained magnetic sub-bands with non-ideal quantum geometric properties,” explained Dr. Oskar Vafek, co-senior author. This interpretation opens exciting opportunities to probe connections between FQH states and fractional Chern insulators in upcoming experiments.

Looking Ahead

Beyond the striking observation of SBCIs and FQH states, this work positions MATBG as a powerful quantum simulator. By combining optical probes, transport measurements, and advanced theories, researchers aim to map the complex phase diagrams of correlated moiré systems. Future directions include exploring light-driven control of topological states and testing the link between fractional Chern insulators and fractional quantum Hall effects.

References

Minhao He et al., Strongly interacting Hofstadter states in magic-angle twisted bilayer graphene, Nature Physics (2025). DOI: 10.1038/s41567-025-02997-4

Original article link: Phys.org

*This blog article was prepared with the help of AI technologies.*

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#Graphene #MagicAngleGraphene #HofstadterButterfly #TopologicalPhases #ChernInsulators #FractionalQuantumHall #MoiréMaterials #QuantumMaterials #NaturePhysics #QuantumServerNetworks

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