Conductance oscillations in two-dimensional Sharvin point contacts

Abstract

The conductance of quantum-mechanical particles through two-dimensional point contacts, with and without impurities, is calculated. It is shown that, even for a zero-length constriction, steplike structures occur at integer multiples of 2$e^2$/h as a function of the constriction width. These step precursors evolve rapidly into horizontal plateaux on increasing the length of the constriction. It is also shown that the effect of impurities is to modify the structures and to shift the value of the conductance at the steps away from the quantized values.