Multiprobe electron waveguides: Filtering and bend resistances

Recent work in high-mobility quantum wires suggests that electron waveguide behavior is relevant for transport at low temperature. We therefore study transport in ideal electron waveguides paying particular attention to their multimode properties. In order to address four-probe measurements, junctions between waveguides must be included and we consider systems with both one and two junctions. We find, first, that the junctions strongly filter the electrons, changing the distribution of the electrons among the modes of the waveguide. Second, the junctions give rise to both substantial longitudinal resistance and bend resistances which can be either local or nonlocal. The latter effect is a direct result of the filtering properties and decays on the length scale of a mean free path in a system with disorder. In a system where the disorder is smooth, the decay of the nonlocal bend resistance occurs over a distance much smaller than the transport mean free path but close to the total mean free path. Third, interference in scattering from two junctions leads to an oscillatory dependence of the transmission on the length between the junctions. The period of this oscillation is surprisingly low, being determined by mixing of the various modes in the waveguide, and shows up strongly in the nonlocal resistance. Finally, throughout this work we compare the quantum results to classical calculations in order to separate classical size effects from effects which require coherence. The classical transmission coefficient approach is derived from the Boltzmann equation with suitable boundary conditions. The basic trends are present in the classical calculations; however, there are large quantum deviations in certain cases as well as some phenomena which are strictly quantum mechanical, especially in the few-mode regime.