Charge sensing of graphene in quantum Hall regime with scanning tunneling microscopy

In the presence of a strong magnetic field, electrons form Landau levels, leading to enhanced interactions that give rise to collective properties, such as fractional excitations and electron solids. Many of the observed phenomena have been successfully explained using the concept of composite fermions, which represent the bound state of an electron with an even number of fluxes and are described by a Chern-Simons gauge field. In this work, we introduce a new experimental technique to visualize the local response of partially filled Landau levels and fractional quantum Hall liquids in monolayer graphene. Utilizing a double-layer device structure, we achieve high-resolution electrostatic potential measurements down to 0.2 meV with spatial precision comparable to the magnetic length. Our experiments reveal localized charge density fluctuations near individual charge impurities with periodicity determined by the magnetic length and charge density. This technique offers a powerful means to probe fractional quantum Hall states and their quasi-particles on the magnetic length scale and holds potential for application in the study of electronic structures in other materials.