Transport studies of localized and extended states of a two-dimensional electron gas in low magnetic fields

We have observed the quantum Hall effect in a high mobility two-dimensional electron gas to filling factors up to 80 at 0.3 K. This demonstrates the presence of both localized and extended states at low field, and explains the failure of the standard semi-classical analysis of Shubnikov-de Haas (SdH) oscillations in this regime. We go on to derive a general expression for the conductivity due to rectangular bands of extended states, and show that the observed temperature dependence of the SdH oscillations is consistent with this picture. An analysis of the oscillations using this expression reveals the predicted levitation of the extended states as the magnetic field is reduced. (C) 1997 Elsevier Science B.V. All rights reserved