Effect of impurities on the quantized conductance of narrow channels

The conductance G of narrow channels has been observed recently to be quantized in integer multiples of 2$e^2$/h. We have calculated G for the case that an impurity is present in the channel. The channel is modeled as an electron waveguide, and the impurity is assumed to be an isotropic (s-like) scatterer. An analytic expression for G is obtained. We find that G is reduced below the unperturbed plateau values, and that for very strong scatterers the plateaus disappear. However, G exhibits two interesting features: First, G is pinned such that whenever the Fermi level is at the band bottom of the (n+1)th transverse subband G=n(2$e^2$/h). Second, for attractive impurity potentials that have phase shift ${\delta }_0$≲30°, the conductance is found to have a deep downward dip between adjacent conductance plateaus. We attribute these features to multiple scattering between the impurity and the waveguide walls.