Although we believe that the charac

Although we believe that the characteristic features of the magnetoresistance anomalies are now understood, several interesting points of disagreement between theory and experiment remain that merit further investigation. One of these is the discrepancy in the magnitude of the negative bend resistance at zero magnetic field noted before. The disappearance of a region of quenched Hall resistance at low electron density is another unexpected observation by Chang et al.375 and Roukes et al.383 The semiclassical theory predicts a universal behavior (for a given geometry) if the resistance and magnetic field are scaled by R0 and B0 defined in Eq. (3.42). For a squarewell confining potential the channel width W is the same at each energy, and since B0 ∝ kF one would expect the field region of quenched Hall resistance to vary with the electron density as √ns. For a more realistic smooth confining potential, W depends on EF and thus on ns as well, in a way that is difficult to estimate reliably. In any case, the experiments point to a systematic disappearance of the quench at the lowest densities, which is not accounted for by the present theory (and has been attributed by Chang et al.375 to enhanced diffraction at low electron density as a result of the increase in the Fermi wavelength). For a detailed investigation of departures from classical scaling, we refer to a paper by Roukes et al.384 As a third point, we mention the curious density dependence of the quenching observed in approximately straight junctions by Roukes et al.,383 who find a low-field suppression of RH that occurs only at or near certain specific values of the electron density. The semiclassical model applied to a straight Hall cross (either defined by a square well or by a parabolic confining potential) gives a low-field slope of RH close to its bulk 2D value. The fully quantum mechanical calculations for a straight junction376,381 do give quenching at special parameter values, but not for the many-mode channels in this experiment (in which quenching occurs with as many as 10 modes occupied, whereas in the calculations a straight cross with more than 3 occupied modes in the channel does not show a quench).