Figure 1

Left panel: Waterfall plot of $R_{xx}$ and $R_{xy}$ traces at different densities for a 42-nm-wide GaAs QW. (a)–(d) Schematic LL diagrams at $\nu =7/2$ for different densities corresponding to the traces marked $\mathbf{a}$–$\mathbf{d}$ in the left panel. The subband separation, cyclotron, and Zeeman energies are marked as $\Delta$, $\hslash {\omega }_c$, and $E_Z$, respectively. Self-consistently calculated charge distributions are shown in the insets to (a) and (d) for $n=2.13$ and $2.96\times {10}^{11}{\mathrm{cm}}^{-2}$.Reuse & Permissions

Figure 2

(a) $R_{xx}$ and $R_{xy}$ traces for a 37-nm-wide GaAs QW at $n=2.34\times {10}^{11}{\mathrm{cm}}^{-2}$ at different tilt angles $\theta$ as depicted in (b). (c) Charge distribution calculated self-consistently at $B=0$. (d) LL diagram at $\theta =0$ at $\nu =7/2$.Reuse & Permissions

Figure 3

(a) $R_{xx}$ and $R_{xy}$ traces for a 55-nm-wide GaAs QW, at a fixed $n=3.62\times {10}^{11}{\mathrm{cm}}^{-2}$, as the charge distribution is made increasingly asymmetric. Values of $\Delta$, measured from low-$B$ Shubnikov–de Haas oscillations, are indicated for each trace. Vertical arrows mark the positions of observed anomalous $R_{xx}$ minima. (b) A color-scale plot of data in (a). Solid and dotted lines are the calculated boundary within which the $S1\text{}\text{}\uparrow$ and $A0\text{}\text{}\uparrow$ levels are pinned together at $E_F$ [24]. The dashed line represents the values of $B$ at which, according to the calculations, the $S1\text{}\text{}\uparrow$ level is half-filled; it tracks the positions of the observed $R_{xx}$ minima marked by vertical arrows in (a). (c)–(e) Schematic LL diagrams (left), charge distributions and potentials (upper right), and wave functions ${\psi }_S$ and ${\psi }_A$ (lower right), self-consistently calculated at $B=0$ (blue) and at $\nu =4$ (red). In (c)–(e), the filling factor of the $S1\text{}\text{}\uparrow$ level equals 0, 0.5, and 1, respectively. In each panel, the calculated wave functions are shifted vertically according to the calculated values of $\Delta$ and $\Delta (B)$.Reuse & Permissions