The most detailed study by far of t

The most detailed study by far of the 2D to 1D crossover of the electron-electron interaction effect in narrow channels was made by Choi et al.55 in a GaAs-AlGaAs heterostructure. In Fig. 27 we reproduce some of their experimental traces for channel widths from 156 to 1.1 μm and a channel length of about 300 μm. The weak localization peak in the magnetoresistance is not resolved in this experiment, presumably because the channels are not in the 1D regime for this effect (the 2D weak localization peak would be small and would have a width of 10−4 T). The negative magnetoresistance that they found below 0.1 − 0.2T in the narrowest channels is temperature-independent between 1 and 4K and was therefore identified by Choi et al.55 as a classical size effect. The classical negative magnetoresistance extends over a field range for which 2lcycl >∼W. This effect has been discussed in Section II.A in terms of reduction of backscattering by a magnetic field. The electronelectron interaction effect is observed as a (temperaturedependent) parabolic negative magnetoresistance above 0.1T for the widest channel and above 0.3T for the narrowest one. From the magnitude of the parabolic negative magnetoresistance, Choi et al.55 could find and analyze the crossover from 2D to 1D interaction effects. In addition, they investigated the cross over to 0D by performing experiments on short channels. As seen in Fig. 27, Shubnikov-De Haas oscillations are superimposed on the parabolic negative magnetoresistance at low temperatures and strong magnetic fields. It is noteworthy that stronger fields are required in narrower channels to observe the Shubnikov-De Haas oscillations, an effect discussed in terms of specular boundary scattering by Choi et al. The Shubnikov-De Haas oscillations in narrow channels are discussed further in Section II.F.2.