Imaging electron density in a two-dimensional electron gas

Spatial profiles of the electron density in a two-dimensional electron gas were obtained from the spacing of interference fringes in coherent electron flow. Images of electron flow from a quantum point contact formed in a GaAs/AlGaAs heterostructure were recorded with a liquid He cooled scanned probe microscope. The images are decorated with interference fringes spaced by half the Fermi wavelength; the fringe spacing measures the electron density below the scanned probe microscope tip. As the density is decreased with a back gate, the fringe spacing increases in agreement with a planar capacitor model.