FIG.52 Illustration of classical el

FIG.52 Illustration of classical electron focusing by a magnetic field. Top: Skipping orbits along the 2DEG boundary. The trajectories are drawn up to the third specular reflection. Bottom: Plot of the caustics, which are the collection of focal points of the trajectories. Taken from H. van Houten et al., Phys. Rev. B 39, 8556 (1989). FIG.53 Bottom: Experimental electron focusing spectrum (T = 50mK, L = 3.0 μm) in the generalized Hall resistance configuration depicted in the inset. The two traces a and b are measured with interchanged current and voltage leads, and demonstrate the injector-collector reciprocity as well as the reproducibility of the fine structure. Top: Calculated classical focusing spectrum corresponding to the experimental trace a (50-nm-wide point contacts were assumed). The dashed line is the extrapolation of the classical Hall resistance seen in reverse fields. Taken from H. van Houten et al., Phys. Rev. B 39, 8556 (1989). FIG.54 Experimental electron focusing spectrum over a larger field range and for very narrow point contacts (estimated width 20–40 nm; T = 50mK, L = 1.5 μm). The inset gives the Fourier transform for B ≥ 0.8T. The high-field oscillations have the same dominant periodicity as the low-field focusing peaks, but with a much larger amplitude. Taken from H. van Houten et al., Phys. Rev. B 39, 8556 (1989). FIG.55 Phase knL of the edge channels at the collector, calculated from Eq. (3.27). Note the domain of approximately linear n-dependence of the phase, responsible for the oscillations with Bfocus-periodicity. Taken from H. van Houten et al., Phys. Rev. B 39, 8556 (1989). FIG.56 Focusing spectrum calculated from Eq. (3.29), for parameters corresponding to the experimental FIG.54. The inset shows the Fourier transform for B ≥ 0.8T. Infinitesimally small point contact widths are assumed in the calculation. Taken from C. W. J. Beenakker et al., Festk¨orperprobleme 9, 299 (1989).