Direct Imaging of Current and Dissipation of Quantum Hall Edge States in Graphene with Scanning Nanoscale SQUID-on-Tip Microscopy

When a strong out of plane magnetic field is applied to a two-dimensional electron system, the electrons in the bulk are localized, while the electrons near the edge remain conductive as the energy bands bend and cross the Fermi level. These conductive edge states are theoretically immune to back scattering and give rise to quantized Hall conductivity, the hallmark of the quantum Hall effect. Here we explore the utility of scanning nanoscale SQUID on tip (nSOT) microscopy for investigating edge state physics, focusing on the current- or doping-induced breakdown of quantization in the integer quantum Hall effect. nSOT microscopy provides direct, non-invasive, nanoscale resolution spatial imaging of current and temperature in ambient magnetic fields up to 2T, matching the regime of integer quantum Hall effects in high mobility graphite-gated graphene heterostructures. I will discuss edge state signal estimates and preliminary measurements made with our newly built 4.2 Kelvin scanning nSOT microscope.