Figure 1

Longitudinal magnetoresistance measured at $T=30$ mK in a 42-nm-wide QW along the [110] ($R_{xx}$, red traces) and [1$\overline{1}$0] ($R_{yy}$, black traces) directions. Data are shown in the filling factor range $6<\nu <8$ at different electron densities as indicated. The field positions of half-filled LLs ($\nu =13/2$ and 15/2) are marked by vertical lines, and the LLs in which $E_F$ resides at the different half fillings are indicated in boxes.Reuse & Permissions

Figure 2

Schematic Landau level energy diagram as a function of density for the 42-nm-wide QW. The relevant energies are the subband separation ($\Delta$), and the cyclotron and Zeeman energies ($\hslash {\omega }_c$ and $E_Z$); the up- ($\uparrow$) and down-spin ($\downarrow$) levels are represented by solid and dashed lines, respectively. The energies are plotted as a function of the field position of filling factor $\nu =13/2$ (bottom axis) and $\nu =15/2$ (top axis). The positions of $E_F$ at $\nu =13/2$ and 15/2 are marked by the green and blue lines, respectively. The triangles labeled $a$ to $f$ point to the positions of $\nu =13/2$ and 15/2 for the densities at which traces are shown in Figs. 1a, 1b, 1c, 1d, 1e, 1f.Reuse & Permissions

Figure 3

(a)–(d) $R_{xx}$ and $R_{yy}$ measured in a 51-nm-wide QW at four different densities as indicated. Solid (dotted) traces were taken while the field was swept down (up). All traces were taken at a sweep rate of 1 T/hour. (e) The LL energy fan diagram corresponding to the data shown in (a)–(d); the notations used are the same as those in Fig. 2.Reuse & Permissions

Figure 4

(a) $R_{xx}$ and $R_{yy}$ taken in the 51-nm-wide QW at a fixed density of $n=2.5\times {10}^{11}$ cm${}^{-2}$ when the QW charge distribution is symmetric. (b)–(c) Traces are shown as the charge distribution in the QW is made asymmetric by transferring $\sim$5$\%$ of total charge from the back side of the QW to the front side (b) or vice versa (c).Reuse & Permissions