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Description:

Charge distribution offers a unique fingerprint of important properties of electronic systems, including dielectric response, charge ordering and charge fractionalization. We develop a new architecture for charge sensing in two-dimensional electronic systems in a strong magnetic field. We probe local change of the chemical potential in a proximitized detector layer using scanning tunneling microscopy (STS), allowing us to infer the chemical potential and the charge profile in the sample. Our technique has both high energy (<0.3 meV) and spatial (<10 nm) resolution exceeding that of previous studies by an order of magnitude. We apply our technique to study the chemical potential of quantum Hall liquids in monolayer graphene under high magnetic fields and their responses to charge impurities. The chemical potential measurement provides a local probe of the thermodynamic gap of quantum Hall ferromagnets and fractional quantum Hall states. The screening charge profile reveals spatially oscillatory response of the quantum Hall liquids to charge impurities, and is consistent with the composite Fermi liquid picture close to the half-filling. Our technique also paves the way to map moiré potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators.

Rights:

• Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International
  

Keyword: charge sensing
, quantum Hall states, scanning tunneling microscopy (STM)


Date published: 2025-02-25

Publisher: Proceedings of the National Academy of Sciences

Journal:

• Proceedings of the National Academy of Sciences (ISSN: 10916490) vol. 122 issue. 8 e2424781122

Funding:

• U.S. Department of Energy DE-FG02-07ER46419
• Gordon and Betty Moore Foundation GBMF 9469
• National Science Foundation DMR-2011750
• National Science Foundation DMR-2312311
• National Science Foundation OMA-2326767.
• DOD | USN | Office of Naval Research ONR N00014-24-1-2471
• DOD | USA | AFC | CCDC | Army Research Office MURI 134396-5117989 (AROW911NF2120147
• U.S. Department of Energy DE-AC02-05-CH11231
• Heising-Simons Foundation Fellowship
• Simons Foundation Fellowship
• Shota Rustaveli National Science Foundation PHY-2309135
• Gordon and Betty Moore Foundation GBMF8688
• Department of Energy and Climate Change DE-AC02-05-CH11231

Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1073/pnas.2424781122

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Updated at: 2026-03-21 15:07:32 +0900

Published on MDR: 2026-03-02 17:20:27 +0900