METHOD TO INVESTIGATE THE RANDOM POTENTIAL IN A QUANTUM POINT-CONTACT

We propose a method of exploring the random potential in the vicinity of a quantum point contact (QPC). The position and parameters of the s addle point of the smooth potential in the QPC are varied by four gate s above the two-dimensional electron gas. Two of them form the QPC and shift the saddle point across the channel. The other two gates are pl aced in the source and drain areas to drive the saddle point along the channel. A resonant tunneling peak appears in the conductance when th e saddle point and a local minimum of the random potential coincide. T he most pronounced peaks appear in the pinch-off regime when the QPC i s classically closed and the Fermi energy of the two-dimensional elect ron gas equals the binding energy in a local minimum. For a quantitati ve description, a simple realistic model of the heterostructure has be en considered. We have assumed that the free surface of the heterostru cture has a pinned potential ana that no charge moves in the doped lay er in response to a gate voltage. A three-dimensional electrostatic pr oblem has been solved for the above situation. The position and other parameters of the saddle point are calculated analytically and a pract ical procedure for determining the parameters of the bound states is p roposed. We also discuss the influence of Coulomb blockade phenomena o n the proposed experiment.