Microwave Imaging of Edge Conductivity in Graphene at Charge Neutrality and Quantum Hall States

TL;DR

This study uses microwave impedance microscopy to image and analyze edge conductivity in graphene at various quantum Hall states, revealing distinct behaviors at charge neutrality and integer fillings.

Contribution

It provides the first detailed microwave imaging of edge states in graphene across different quantum Hall regimes, linking local conductivity profiles to theoretical models.

Findings

Edge conductivity at charge neutrality decreases slowly with magnetic field.

Distinct evolution of edge signals between ν=0 and |ν|≥1 states.

Microscopic picture of edge and bulk states across Landau levels.

Abstract

We report local conductivity imaging of edge states in monolayer graphene by millikelvin microwave impedance microscopy (MIM). At the charge-neutrality point, as the magnetic field increases, the local conductivity at the edge drops to zero more slowly than in the bulk. This behavior is consistent with the calculated spatial profile of the charge gap in the canted antiferromagnetic phase. For comparison, we also perform microwave imaging of integer quantum Hall states away from neutrality, which host dissipationless chiral edge channels. The evolution of the edge signal as a function of the bulk gap is fundamentally different between the Landau level filling factor $\nu = 0$ and $|\nu| \ge 1$ integer quantum Hall states, which can be qualitatively explained by numerical simulations and theoretical analysis. Our results provide a comprehensive microscopic picture of the edge and bulk states as the Fermi level moves across the unique Landau-level spectrum of graphene.