The conclusions of the previous par

The conclusions of the previous paragraph have interesting implications for the Shubnikov-De Haas oscillations in the strong-field regime even if measured with contacts that do not selectively detect certain edge channels only.307 Consider again the geometry of Fig. 92, in the low-gate voltage limit where the point contact voltage probe transmits all edge channels with unit probability. (This is the case of an “ideal” contact; cf. Section IV.A.2.) To simplify expression (4.21) for the threeterminal longitudinal resistance R3t, we use the fact that the transmission and reflection probabilities Ts→p, Rs, and Rp refer to the highest-index edge channel only (with index n = N), under the assumptions of selective backscattering and absence of scattering to lowerindex edge channels discussed earlier. As a consequence, Ts→p,Rs, and Rp are each at most equal to 1; thus, up to corrections smaller by a factor N−1, we may put these terms equal to zero in the denominator on the right-hand side of Eq. (4.21). In the numerator, the transmission probability Ts→p may be replaced by the backscattering probability tbs ≤ 1, which is the probability that the highest-index edge channel injected by the source contact reaches the point contact probe following scattering across the wide 2DEG (dashed lines in Fig. 92). With these simplifications Eq. (4.21) takes the form (assuming spin degeneracy)