Nanoscale Imaging of Quantum Hall Currents
In the Hall effect, the quantum Hall effect, and other magnetotransport regimes, the spatially averaged voltages and currents are typically measured with terminals attached to the sides of a sample. Mapping the electrons’ paths—that is, imaging the current flows themselves—requires a nanoscale probe. Now Zachary Krebs of the University of Wisconsin-Madison and his collaborators have adapted a 40-year-old technique, scanning tunneling potentiometry, to image current flows in a square sheet of graphene in an out-of-plane magnetic field [1]. They found three distinct flow regimes, one of which surprised them.
The graphene sheet was clean enough to ensure that it was mostly free of impurities that could scatter the electrons. However, the electrons did have to circumvent a central, circular, electrostatic barrier that the researchers created with the charged tip of a scanning tunneling microscope.
At low magnetic fields, the electrons’ cyclotron diameter—the size of the circles electrons trace as they move in a magnetic field—exceeded the sample size, and the electrons behaved ballistically, bouncing off the central barrier. At moderate fields, the cyclotron diameter was smaller than the sample yet larger than the electrons’ mean free path, and the electrons behaved as if they encountered ohmic resistance and flowed in spirals around the barrier. At high fields, when the cyclotron diameter was smaller than the mean free path, Krebs and his collaborators expected that the slow drift velocity would give the electrons plenty of time to scatter and bounce off the barrier. Instead, they flowed ballistically in circular, cycloid-like trajectories around the barrier. From their calculations, the researchers concluded that the formation of quantized Landau levels suppressed the bouncing and preserved ballistic transport.
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- Z. J. Krebs et al., “Nanoscale imaging of magnetotransport around a circular p-n junction in graphene,” Phys. Rev. Lett. 136, 136301 (2026).