Quantum point contacts represent, in many regards, the simplest system in mesoscopic physics. By applying a voltage to a gate electrode (see the inset of figure 1), researchers can control the width of a constriction between two reservoirs of electrons in a two-dimensional electron gas (2DEG). For sufficiently large negative gate voltages, the constriction is completely closed off, and electrons must tunnel between the reservoirs. But when the voltage is made less negative, the constriction begins to open up, and the conductance through the quantum point contact increases in steps of 2e 2/h (see the article by Henk van Houten and Carlo Beenakker in Physics Today, Physics Today 0031-9228 49 7 1996 22 https://doi.org/10.1063/1.881503 July 1996, page 22 ).
The origin of this quantized conductance is neatly explained using a model of noninteracting electrons. The constriction lets through an integer number of transverse modes, each...
