Scanning Microscopes Probe Local Details of the Quantum Hall State

Abstract

Since the discovery of the integer quantum Hall effect in 1980, many physicists have been intrigued by this special state, in which electrons confined in a two‐dimensional world execute tiny orbits about magnetic flux lines. Much as we may want to visualize its microscopic structure, however, most of what we have learned to date about the quantum Hall state is based on measurements of bulk properties such as the Hall conductance. Microscopic measurements of more local properties have eluded us because the electrons that form the quantum Hall state reside at an interface between semiconducting layers that are buried tens of nanometers below the surface. And the quantum Hall behavior shows up only when the sample is cooled to temperatures below a few kelvin and placed in a high magnetic field, on the order of several teslas.