Conductance of quantum point contacts in the presence of disorder

We have calculated the conductance of a two-dimensional electron gas through single and double constrictions using a mode-matching technique. In order to take into account the smooth variation of the confinement potential, and the presence of disorder, the calculation is made within a lattice model. We find that the conductance at plateaus is reduced below the quantized values if short-range scatterers are introduced in the channel. However, the conductance remains well quantized even in the presence of long-range impurities. These observations explain the suppression of conductance time-dependent fluctuations at plateaus experimentally observed by Timp et al. [Phys. Rev. B 42, 9259 (1990)]. We also examine the effects of impurities on the resonant transmission properties through a single quantum dot. As the disorder is introduced, the resonances are broadened in energy and can appear as either peaks or dips depending on the strength of the disorder.