Quantum versus semiclassical analysis of the conductivity of two-dimensional electrons in a magnetic field

We present experimental evidence for the levitation of extended states of a two-dimensional electron system in a magnetic field, and establish the presence of alternating regions of localized and extended states in the density of states to Landau-level filling factors ~n! as high as 80. Monitoring the Hall voltage of a modulationdoped GaAs/AlxGa12xAs heterojunction at fixed magnetic field during continuous illumination from lightemitting diodes reveals a steplike structure with plateaus at even integer n between 22 and 80 at a temperature of 0.3 K. We derive a general expression for the conductivity due to rectangular bands of extended states, and show that the observed temperature dependence of the Shubnikov–de Haas oscillations is consistent with this picture. An analysis of the oscillations using this expression reveals the predicted levitation of the extended states. @S0163-1829~97!05140-0#