Method to investigate the random potential in a quantum point contact.

Abstract

We propose a method of exploring the random potential in the vicinity of a quantum point contact (QPC). The position and parameters of the saddle point of the smooth potential in the QPC are varied by four gates 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 placed in the source and drain areas to drive the saddle point along the channel. A resonant tunneling peak appears in the conductance when the saddle point and a local minimum of the random potential coincide. The most pronounced peaks appear in the pinch-off regime when the QPC is classically closed and the Fermi energy of the two-dimensional electron gas equals the binding energy in a local minimum. For a quantitative description, a simple realistic model of the heterostructure has been considered. We have assumed that the free surface of the heterostructure has a pinned potential and that no charge moves in the doped layer in response to a gate voltage. A three-dimensional electrostatic problem has been solved for the above situation. The position and other parameters of the saddle point are calculated analytically and a practical procedure for determining the parameters of the bound states is proposed. We also discuss the influence of Coulomb blockade phenomena on the proposed experiment.