Transport in an Electron Waveguide

Abstract

An electron waveguide is a wire that is so clean and so small that electron waves can propagate coherently in guided modes, which are characteristic of the geometry, with minimal scattering. An electron waveguide is supposed to be reminiscent of an optical or microwave waveguide, but unlike an electromagnetic wave, an electron wave is sensitive to an applied electric or magnetic field because it possesses a charge. In response to an applied electric field (or to an applied current), an electron waveguide has a resistance which is related to the quantum mechanical transmission through the wire [1]. The transmission probability is affected by both elastic and inelastic scattering. Elastic scattering, such as might occur at an impurity for example, changes the distribution of the electrons between the modes of the guide, but it is phase deterministic; i.e. information associated with the phase of the electronic wave is not ruined by an elastic scattering event. In contrast, inelastic scattering destroys the phase memory in the wave. Coherent electronic transport is possible whenever the wire is smaller than the inelastic scattering length, whether or not there is elastic scattering [2]. Only when a device is smaller than both the inelastic and the elastic scattering lengths and comparable to the wavelength, like it is in an electron waveguide, is the modal distribution of the current important.