From semiclassical transport to quantum Hall effect under low-field   Landau quantization
  The crossover from the semiclassical transport to quantum Hall effect is studied by examining a two-dimensional electron system in an AlGaAs/GaAs heterostructure. By probing the magneto-oscillations, it is shown that the semiclassical Shubnikov-de Haas (SdH) formulation can be valid even when the minima of the longitudinal resistivity approach zero. The extension of the applicable range of the SdH theory could be due to the damping effects resulting from disorder and temperature. Moreover, we observed plateau-plateau transition like behavior with such an extension. From our study, it is important to include the positive magnetoresistance to refine the SdH theory. 
D. R. Hang, C. F. Huang, Y. W. Zhang, H. D. Yeh, J. C. Hsiao, and H.   L. Pang