FIG.45 (a) Classical ballistic tran

FIG.45 (a) Classical ballistic transport through a point contact induced by a concentration difference δn, or electrochemical potential difference eV , between source (s) and drain (d). (b) The net current through a quantum point contact is carried by the shaded region in k-space. In a narrow channel the allowed states lie on the horizontal lines, which correspond to quantized values for ky = ±nπ/W, and continuous values for kx. The formation of these 1D subbands gives rise to a quantized conductance. Taken from H. van Houten et al., in “Physics and Technology of Submicron Structures” (H. Heinrich, G. Bauer, and F. Kuchar, eds.). Springer, Berlin, 1988; and in “Nanostructure Physics and Fabrication” (M. Reed and W. P. Kirk, eds.). Academic, New York, 1989. FIG.46 Transmission resonances exhibited by theoretical results for the conductance of a quantum point contact of abrupt (rectangular) shape. A smearing of the resonances occurs at nonzero temperatures (T0 = 0.02EF/kB ≈ 2.8K). The dashed curve is an exact numerical result; the full curves are approximate. Taken from A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989). FIG.47 Resistance as a function of gate voltage for an elongated quantum point contact (L = 0.8 μm) at temperatures of 0.2, 0.4, and 0.8 K, showing transmission resonances. Subsequent curves from the bottom are offset by 1 k. Taken from R. J. Brown et al., Solid State Electron. 32, 1179 (1989).