Imaging coherent electron wave flow in a two-dimensional electron gas

We measure the energy distribution of electrons passing through a two-dimensional electron gas using a scanning probe microscope (SPM). We present direct spatial images of coherent electron wave flow from a quantum point contact formed in a GaAs/AlGaAs two-dimensional electron gas using a liquid He cooled SPM. A negative voltage is placed on the tip, which creates a small region of depleted electrons that backscatters electron waves. Oscillating the voltage on the tip and locking into this frequency gives the spatial derivative of electron flow perpendicular to the direction of current flow. We show images of electron flow using this method. By measuring the amount of electrons backscattered as a function of the voltage applied to the tip, the energy distribution of electrons is measured.