As a result, ρ xx ~ ρ xy can occur on both sides of B c as seen clearly in Figure 2d. Interestingly, in the crossover from SdH oscillations to the QH state, we observe additional T-independent points, labeled by circles in Figure 2 for each V g, other than the one corresponding to the onset of strong localization. As shown in Figure 2a selleck chemical for V g = −0.125 V, the resistivity peaks at

around B = 0.73 and 1.03 T appear to move with increasing T, a feature of the scaling behavior [7] of standard QH theory around the crossing points B = 0.70 and 0.96 T, respectively. Therefore, survival of the SdH theory for 0.46 T ≤ B ≤ 1.03 T reveals that semiclassical metallic transport may coexist with quantum localization. The superimposed background MR may be the reason for this coexistence, which is demonstrated by the upturned deviation from the parabolic dependence as shown in Figure 2a [45]. Therefore, it is reasonable to attribute the overestimated μ′ shown by the blue symbols in Figure 5a to the influence of the background MR. Similar behavior can also be found for V g this website = −0.145 V even though spin splitting is NSC 683864 mw unresolved, indicating that the contribution of background MR mostly comes from semiclassical effects. However, such a crossing point cannot be observed for V g = −0.165 V since there is no clear separation between extended and localized

states with strong disorder. Only a single T-independent point corresponding to the onset of strong localization occurs at B = 1.12 T. In order to check the validity of our present results, further experiments were performed on a device (H597) with nominally T-independent Hall slope at different applied gate voltages [27]. As shown in Figure 7a for V g = −0.05 V, weakly insulating

behavior occurs as B < 0.62 T ≡ B c, which corresponds to the direct I-QH transition since there is no evidence of the ν = 1 or ν = 2 QH state near B c. The crossing of ρ xx and ρ xy is found to occur at B ~ 0.5 T which is smaller than B c. As we decrease V g to −0.1 V, thereby increasing the effective amount of disorder in the 2DES, the relative positions between these two fields remain the same as shown in Figure 7b. Nevertheless, it can be observed that ρ xy tends to move closer to ρ xx with decreasing Suplatast tosilate V g. This may be quantified by defining the ratio ρ xy/ρ xx at B c, whose value is 1.57 and 1.31 for V g = −0.05 and −0.1 V, respectively. Figure 7 ρ xx and ρ xy as functions of B at various T ranging from 0. 3 to 2 K. For (a) V g = −0.05 V and (b) V g = −0.1 V. The interaction-induced parabolic NMR can be observed at both gate voltages. This result, together with the negligible T dependence of the Hall slope as shown in Figure 8a, implies that the ballistic part of the e-e interactions dominates as mentioned above.