The low-field Hall resistance chang

The low-field Hall resistance changes drastically if the channel width becomes smaller, relative to the radius of curvature of the corners. Figure 67a shows experimental data by Ford et al.77 The solid and dotted curves are for the geometries shown respectively in the upper left and lower right insets of Fig. 67a. Note that these insets indicate the gates with which the Hall crosses are defined electrostatically. The equipotentials in the 2DEG will be smoother than the contours of the gates. The experiment shows a well-developed Hall plateau with superimposed fine structure. At small positive fields RH is either quenched or negative, depending on the geometry. The geometry is seen to affect also the width of the Hall plateau but not the height. In Fig. 67b we give the results of the semiclassical theory for the two geometries in the insets, which should be reasonable representations of the confining potential induced by the gates in the experiment. In the theoretical plot the resistance and the magnetic field are given in units of