The assumption of a single disorder

The assumption of a single disordered probe, plus absence of interedge channel scattering from constriction to probe, thus explains the observation in Fig. 86 of an anomalously high quantum Hall resistance for large gate voltages, such that Nmin < Nwide. Indeed, the experimental Hall resistance for Vg = −2.5V has a plateau around 2.2T close to the value RH = (h/2e2)N−1min (with Nmin = 2), in agreement with Eq. (4.16) if Nl2 ≤ Nmin at this gate voltage. This observation demonstrates the absence of interedge channel scattering over 100 μm (the separation of constriction and probe), but only between the highest-index channel (with index n = Nwide = 3) and the two lower-index channels. Since the n = 1 and n = 2 edge channels are either both empty or both filled (cf. Fig. 87, where these two edge channels lie closest to the sample boundary), any scattering between n = 1 and 2 would have no measurable effect on the resistances. As discussed in Section IV.B.3, we know from the work of Alphenaar et al.429 that (at least in the present samples) the edge channels with n ≤ Nwide − 1 do in fact equilibrate to a large extent on a length scale of 100 μm.