Quantum Hall effect gains a new twist in graphene moiré systems

The nonlinear Hall oscillations in twisted double bilayer graphene. Credit: arXiv DOI: 10.48550/arxiv.2605.05681

Physicists have long been drawn to the nonlinear Hall effect: a subtle variant of the classical Hall effect, in which an electric voltage appears perpendicular to a current flowing through a material. Unlike its classical counterpart, the nonlinear version can arise even without breaking time-reversal symmetry, and its magnitude is tied to deep geometric properties of electron wave functions. So far, however, the behavior of the effect when a magnetic field is applied has remained poorly understood.

Through new research published in Physical Review Letters , a team led by Jinrui Zhong at the Beijing Institute of Technology has shed new light on this question—leading them to discover an entirely new class of quantum oscillation.

Geometry-dependent properties

The second-order nonlinear Hall effect occurs in atom-thick 2D crystals that lack "inversion symmetry"—meaning they look different when flipped through their center. In these materials, charge carriers can occupy asymmetric energy states, causing a Hall voltage that scales with the square of the current rather than varying linearly with it.

The size of this effect is linked to the " Berry curvature ," a geometric property that captures how electron wave functions twist and bend as conditions in the material change. As a result, measurements of the nonlinear Hall effect offer a window into the underlying quantum geometry of electrons, which is increasingly recognized as central to the exotic behavior of many modern quantum materials.

Applying a field

In their study, Zhong's team proposed a new type of quantum oscillation arising from the nonlinear Hall effect in graphene moiré systems : materials made from stacked graphene layers twisted relative to each other. This twist creates a larger repeating atomic structure, which makes the material extremely sensitive to magnetic fields.

As the applied magnetic field is varied, a special condition is periodically met where electrons reorganize into new quantum states occupied by exotic quasiparticles—which behave as though the magnetic field around them has effectively switched off. Through their experiments, the team found that the nonlinear Hall signal oscillated in step with these recurring conditions.

Probing exotic phases

At periodic magnetic field strengths, Zhong's team found that the Hall signal was dominated by the quantum geometric properties of the quasiparticles themselves—specifically, their contributions from Berry curvature. This provided the first direct experimental evidence for the topological nature of these quasiparticles, confirming theoretical predictions about their behavior.

Beyond establishing a new type of quantum oscillation, the results point toward a powerful new way of probing exotic phases of matter. One promising target is the " Wigner crystal ": a frozen lattice of electrons that can spontaneously form at low temperatures and densities.

Ultimately, they could bring physicists a step closer to untangling the dynamics of coexisting quantum phases, perhaps leading to a deeper understanding of the bizarre behaviors they can display.

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Publication details

Jinrui Zhong et al, Nonlinear Hall Quantum Oscillations to Probe Topological Brown-Zak Fermions in Graphene Moiré Systems, Physical Review Letters (2026). DOI: 10.1103/ydym-5t5p On arXiv : DOI: 10.48550/arxiv.2605.05681

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