Model calculations of the quantum ballistic transport in two-dimensional constriction-type microstructures

We describe an exact formalism for the calculation of the zero-temperature dc conductance of various constriction-type microstructures connected to a two-dimensional half plane on both sides. From our results we obtain quantized conductance as a function of constriction width at integer multiples of 2$e^2$/h for constrictions shorter than a Fermi wavelength. For longer constrictions, the conductance oscillates below the quantized values. The effect of impurities is to destroy quantization if the impurities are within a few wavelengths of the aperture. We show that there is a weak diffraction pattern in the transmitted electronic amplitude superimposed on the classical cos(α) behavior.