4. Suppression of the Shubnikov-De

4. Suppression of the Shubnikov-De Haas oscillationsShubnikov-De Haas magnetoresistance oscillations were discussed in Sections I.D.3 and II.F. In weak magnetic fields, where a theoretical description in terms of a local resistivity tensor applies, a satisfactory agreement between theory and experiment is obtained.20 As we now know, in strong magnetic fields the concept of a local resistivity tensor may break down entirely because of the absence of local equilibrium. A theory of the Shubnikov-De Haas effect then has to take into account explicitly the properties of the contacts used for the measurement. The resulting anomalies are considered in this subsection. Van Wees et al.428 found that the amplitude of the high-field Shubnikov-De Haas oscillations was suppressed if a quantum point contact was used as a voltage probe. To discuss this anomalous Shubnikov-De Haas effect, we consider the three-terminal geometry of Fig. 92, where a single voltage contact is present on the boundary between source and drain contacts. (An alternative twoterminal measurement configuration is also possible; see Ref.428.) The voltage probe p is formed by a quantum point contact, while source s and drain d are normal ohmic contacts. (Note that two special contacts were required for the anomalous quantum Hall effect of Section IV.B.3.) One straightforwardly finds from Eq. (3.12) that the three-terminal resistance R3t ≡ (μp − μd)/eI measured between point contact probe and drain is given by