Landau-level mixing, floating-up extended states, and scaling behavior in a GaAs-based two-dimensional electron system containing self-assembled InAs dots*

Temperature-driven flow lines corresponding to Landau level filling factor $\nu=2 \sim 4$ were studied in the $\sigma_{xx}-\sigma_{xy}$ plane in a GaAs-based two-dimensional electron system with self-assembled InAs dots. In the insulator-quantum Hall (I-QH) transition resulting from the floating-up extended states, the flow diagram showed the validity of the scaling and we observed the expected semicircle. On the other hand, the curve $\sigma_{xx}(\sigma_{xy})$ in the low-field insulator demonstrated the existence of Landau-level mixing. By decreasing the effective disorder, we found that such flow lines can leave the I-QH regime and follow the scaling for the plateau transition between $\nu =4$ and 2. The semicircle in the observed I-QH transition, in fact, originated from the distortion on the plateau-transition curve due to Landau-level mixing. Our study showed the importance of the level-mixing effects to the scaling and semicircle law as the extended states float up.