Classical and quantum ballistic-transport anomalies in microjunctions

Abstract

We have performed quantum-mechanical and classical calculations of the magnetotransport behavior of two-dimensional four-terminal junctions in the ballistic regime. Experimentally, these systems exhibit magnetotransport anomalies at small fields, suppression (quenching) of the Hall resistance, and enhanced bend resistance, which we have reproduced with our model calculations. Because the structures are ballistic, scattering from geometric features of the junction are responsible for the anomalous transport behavior. We study several different kinds of junction (including those with soft and hard walls) and find that their Hall and bend resistances are extremely sensitive to the geometry of the junction. Analysis of our results leads to three major conclusions. (1) In all cases where quenching or inversion of the Hall resistance occurs, or where there is a large bend resistance at zero magnetic field, collimation of the injected electrons is important. Collimation means that the momentum distribution of injected electrons is weighted towards large parallel momentum due to a gradual widening of the wires near the junction. (2) The resistances obtained from the classical and quantum-mechanical calculations differ substantially. First, the quantum-mechanical result at zero temperature is strikingly different from the classical result because of large fluctuations caused by interference between long paths. Such effects are suppressed by temperatures of order 1 K and have been treated elsewhere. In this work we focus on the average quantum-mechanical behavior, which we extract by two different averaging procedures. The classical and quantum-mechanical results are in good qualitative agreement; however, we find substantial quantitative differences that persist well into the many-channel (classical) limit. (3) We analyze the classical results in terms of the type of electron trajectory that contributes to the Hall or bend resistance and find that the ballistic anomalies are caused by short trajectories. In particular, we find that long scrambling trajectories are not important in producing these anomalies. These conclusions are reinforced and illustrated by quantum-mechanical calculations of local transport quantities: the charge density, the current density, and the Wigner and Husimi distributions. The collimation of the injected electrons and the importance of specific short trajectories are particularly clear in the Wigner and Husimi distributions. © 1991 The American Physical Society.