Introduction to Quantum Transport in Electron Waveguides

Abstract

A number of exciting low-dimensional semiconductor devices and structures have been fabricated recently where the key feature is the confinement of the conducting electrons to narrow channels which have dimensions comparable to or smaller than the inelastic coherence length at an appropriate temperature. The most interesting devices possess some feature sizes commensurate with the de Broglie wavelength. Examples of such structures include quantum wires, ring structures and split-gate squeezed channel devices. To a certain extent these structures may be pictured as electron waveguides. Originally of interest for the construction of electron interferometer devices, a number of phenomena have been discovered in electron waveguides which bring out more of the classical picture of the electron than had been originally appreciated: particulary focussing effects and the cycloidal motion peculiar to magnetic edge states. As we shall see in this chapter even the phenomenon of conductance quantization in quantum point contacts depends more on the quantization of the carrier supply function than on an intrinsic quantum transport process. This paradox may be understood on the basis of rigorous quantum transport theory. Although practical devices are much further from development than had been hoped for in the mid-nineteen eighties, electron waveguide structures offer one route to the study and possible application of granular electronics. Indeed they provide an environment for exposing some outstanding difficulties with manipulating devices containing very few carriers.