Synchronous multi-technique scanning mode for probing spatially distributed quantum Hall effect in graphene

Abstract Quantum Hall effect (QHE) in graphene has been widely studied due to its simple device architecture, modest cryogenic requirements, and the unique non-equidistant Landau-level spectrum of Dirac carriers. Real-space visualization of the QHE in graphene is essential both for elucidating fundamental physics and for guiding graphene-based device design. Here, we present a novel scanning approach termed parallel EFM-sMIM imaging (PEMI) mode, which combines electrostatic force microscopy (EFM) and scanning microwave impedance microscopy (sMIM) to investigate the spatially distributed QHE in graphene. Comparative analysis reveals that the single-pass EFM mode demonstrates superior spatial resolution and signal-to-noise ratio compared to the constant-height EFM mode. PEMI measurements reveal that graphene’s electrical conductance manifests as discrete island-like domains exhibiting remarkable stability against magnetic field variations, and spatially distributed QHE states demonstrate independent emergence and evolution within these conductance islands. Notably, while tip-bias compensation demonstrates effectiveness in mitigating crosstalk interference, this technique inherently presents a trade-off by compromising the resolution of EFM signals. Finally, we employ contact-mode sMIM to measure carrier density and determine carrier type. This framework establishes a novel paradigm for parallel characterization of QHE textures and demonstrates promising extensibility to diverse 2D electronic systems through its adaptable architecture.