It is often said that nanostructures have become the system of choice for studying transport over the past few years. What does this simple statement mean?

First, consider transport in large, macroscopic systems. Quite simply, for the past fourscore years, emphasis in studies of transport has been on the Boltzmann transport equation and its application to devices of one sort or another. The assumptions that are usually made for studies are the following: (i) scattering processes are local and occur at a single point in space; (ii) the scattering is instantaneous (local) in time; (iii) the scattering is very weak and the fields are low, such that these two quantities form separate perturbations on the equilibrium system; (iv) the time scale is such that only events that are slow compared to the mean free time between collisions are of interest. In short, one is dealing with structures in which the potentials vary slowly on both the spatial scale of the electron thermal wavelength (to be defined below) and the temporal scale of the scattering processes.

In contrast to the above situation, it has become possible in the last decade or so to make structures (and devices) in which characteristic dimensions are actually smaller than the appropriate mean free paths of interest. In GaAs/GaAlAs semiconductor heterostructures, it is possible at low temperature to reach mobilities of 106 cm2/Vs, which leads to a (mobility) mean free path on the order of 10 μm and an inelastic (or phase-breaking) mean free path even longer. (By “phase-breaking” we mean decay of the energy or phase of the “wave function” representing the carrier.)