Semi-Classical Theory of Magnetoresistance Anomalies in Ballistic Multi-Probe Conductors

Abstract

The regime of ballistic transport in a two-dimensional electron gas (2DEG) was opened up a few years ago, when it became possible technically to reduce the dimensions of a conductor to below a mean free path. In this regime the resistance is determined by the geometry of the conductor, to the extent that impurity scattering can be neglected. In the usual regime of diffusive transport, the Hall bar geometry (a straight current-carrying channel with small side contacts for voltage drop measurements) is most convenient to determine the various components of the resistivity tensor separately. A down-scaled Hall bar was therefore the natural first choice as a geometry to study ballistic transport in a 2DEG (Timp et al., 1987; Roukes et al., 1987; Takagaki et al., 1988; Simmons et al., 1988; Chang et al., 1988; Ford et al., 1988). The point contact geometry (a short and narrow constriction) was an alternative choice (Van Wees et al., 1988; Wharam et al., 1988; Van Houten et al., 1988a). As it turns out, it is much easier to understand ballistic transport through a point contact than through a narrow Hall bar. The reason is that the resistance of a point contact is determined mainly by the number of occupied 1-dimensional subbands at the narrowest point of the constriction, and not so much by its shape (cf. the very similar results of Van Wees et al. (1988) and Wharam et al. (1988) on the quantized resistance of point contacts of a rather different design). The resistances measured in a narrow channel geometry, in contrast, are mainly determined by scattering at the junction with the side probes (Timp et al., 1988), which is different for junctions of different shape. The strong dependence of the low-field Hall resistance on the junction shape was demonstrated theoretically by Baranger and Stone (1989), and experimentally by Ford et al. (1989a) and Chang et al. (1989).