High spatial resolution charge sensing of quantum Hall states

TL;DR

This paper introduces a high-resolution charge sensing technique using scanning tunneling microscopy to study quantum Hall states in graphene, revealing detailed charge profiles and responses to impurities with unprecedented spatial and energy resolution.

Contribution

The authors develop a novel charge sensing method with high spatial and energy resolution, enabling detailed local measurements of quantum Hall states in two-dimensional materials.

Findings

Detected spatial oscillations in charge response near impurities.

Measured local chemical potential variations in quantum Hall liquids.

Confirmed the composite Fermi liquid behavior near half-filling.

Abstract

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 moir\'e potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators.