Topographic Mapping of the Quantum Hall Liquid Using a Few-Electron Bubble

The scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded two-dimensional electron gas. Under quantum Hall effect conditions, applying a positive voltage to the tip locally enhanced the 2D electron density and created a "bubble" of electrons in an otherwise unoccupied Landau level. As the tip scanned along the sample surface, the bubble followed underneath. The tip sensed the motions of single electrons entering or leaving the bubble in response to changes in the local 2D electrostatic potential.

Magnetic field evolution of a 4x4 microns SCA image. Magnetic field ranges from 6.35 Tesla (filling factor ν 1 in the bulk) with a step of 0.05 Tesla between successive frames. The tip voltage is fixed at +1V with respect to the 2DEG. As a result, a bubble of enhanced electron density forms underneath the tip and is dragged inside the 2DEG as the tip is scanned above the sample surface. The bubble is separated from the bulk by an incompressible strip at filling factor ν = 1. Electrons may tunnel across the strip in response to changes the local electrostatic potential of the 2DEG. The signal, governed by Coulomb blockade across the strip, exhibits a series of maxima and minima that result in the observed contour lines that map the random electrostatic potential in the 2DEG. As the field decreases, the position of the strip changes and the contour lines eventually disappear when more than one spin-split Landau level is filled in the bulk (ν >1).