1. MechanismsThe variety of magneto

1. MechanismsThe variety of magnetoresistance anomalies mentioned can be understood in terms of a few simple characteristics of the curved trajectories of electrons in a classical billiard in the presence of a perpendicular magnetic field.359,360 At very small magnetic fields, collimation and scrambling are the key concepts. The gradual widening of the channel on approaching thejunction reduces the injection/ acceptance cone, which is the cone of angles with the channel axis within which an electron is injected into the junction or within which an electron can enter the channel coming from the junction. This is the horn collimation effect329 discussed in Section III.D.1 (see Fig. 65a). If the injection/acceptance cone is smaller than 90., then the cones of two channels at right angles do not overlap. That means that an electron approaching the side probe coming from the main channel will be reflected (Fig. 65a) and will then typically undergo multiple reflections in the junction region (Fig. 65b). The trajectory is thus scrambled, whereby the probability for the electron to enter the left or right side probe in a weak magnetic field is equalized. This suppresses the Hall voltage. This 乬scrambling乭 mechanism for the quenching of the Hall effect requires a weaker collimation than the 乬nozzle乭 mechanism put forward by Baranger and Stone358 (we return to both these mechanisms in Section III.E.3). Scrambling is not effective in the geometry shown in Fig. 65c, in which a large portion of the boundary in the junction is oriented at approximately 45. With the channel axis. An electron reflected from a side probe at this boundary has a large probability of entering the opposite side probe. This is the 乬rebound乭 mechanism for a negative Hall resistance proposed by Ford et al.77