FIG.62 Calculated angular injection

FIG.62 Calculated angular injection distributions in zero magnetic field. The solid histogram is the result of a simulation of the classical trajectories at the Fermi energy in the geometry shown in the inset of FIG.61. The dotted curve follows from the adiabatic approximation (3.31), with the experimental collimation factor f = 1.85. The dashed curve is the cosine distribution in the absence of any collimation. Taken from L. W. Molenkamp et al., Phys. Rev. B. 41, 1274 (1990). FIG.63 Electrostatic focusing onto a collector (C2) of an injected electron beam (at i) by means of a concave lens corresponding to a region of reduced electron density. Focusing in such an arrangement was detected experimentally.350 FIG.64 Magnetic field dependence of the series conductance of two opposite point contacts (measured as shown in the inset; the point contact separation is L = 1.0 μm) for three different values of the gate voltage (solid curves) at T = 100mK. For clarity, subsequent curves from bottom to top are offset by 0.5 × 10−4 −1, with the lowest curve shown at its actual value. The dotted curves are calculated from Eqs. (3.39) and (2.62), with the point contact width as adjustable parameter. Taken from A. A. M. Staring et al., Phys. Rev. B. 41, 8461 (1990). FIG.65 Classical trajectories in an electron billiard, illustrating the collimation (a), scrambling (b), rebound (c), magnetic guiding (d), and electron focusing (e) effects. Taken from C. W. J. Beenakker and H. van Houten, in “Electronic Properties of Multilayers and Low-Dimensional Semiconductor Structures” (J. M. Chamberlain, L. Eaves, and J. C. Portal, eds.). Plenum, London, 1990. FIG.66 Hall resistance as measured (solid curve) by Simmons et al.,178 and as calculated (dashed curve) for the hardwall geometry in the inset (W = 0.8 μm and EF = 14meV). The dotted line is RH in a bulk 2DEG. Taken from C. W. J. Beenakker and H. van Houten, in “Electronic Properties of Multilayers and Low-Dimensional Semiconductor Structures” (J. M. Chamberlain, L. Eaves, and J. C. Portal, eds.). Plenum, London, 1990. FIG.67 Hall resistance as measured (a) by Ford et al.77 and as calculated (b). In (a) as well as in (b), the solid curve corresponds to the geometry in the upper left inset, the dotted curve to the geometry in the lower right inset. The insets in (a) indicate the shape of the gates, not the actual confining potential. The insets in (b) show equipotentials of the confining potential at EF (thick contour) and 0 (thin contour). The potential rises parabolically from 0 to EF and vanishes in the diamond-shaped region at the center of the junction. Taken from C. W. J. Beenakker and H. van Houten, in “Electronic Properties of Multilayers and Low-Dimensional Semiconductor Structures” (J. M. Chamberlain, L. Eaves, and J. C. Portal, eds.). Plenum, London, 1990.