Figure 1

Resistivity vs magnetic field traces for sample A. (a) Temperature dependence of traces is shown; the total bilayer density is $p_{\mathrm{t}\mathrm{o}\mathrm{t}}=4.9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, with both layers having equal densities. The vertical arrow points to the insulating phase developing near the filling factor $\nu =1.1$. (b) Data at $T=30\mathrm{m}\mathrm{K}$ for different values of the charge transfer, $\Delta p$, while $p_{\mathrm{t}\mathrm{o}\mathrm{t}}$ is kept constant at $4.9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$. (c) Data at $T=30\mathrm{m}\mathrm{K}$ at slightly larger total density of $5.5\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, revealing the development of a hysteresis in the magnetoresistance near total filling $\nu =2$ when the bilayer is imbalanced. The upper trace is shifted by $1.5\mathrm{k}\Omega$ for clarity. The right (left) tick mark in the lower trace indicates the expected position of $\nu =1$ for the layer with larger (smaller) density.Reuse & Permissions

Figure 2

${\rho }_{xx}$ vs $B$ traces, at different temperatures for sample B at a total density of $3.9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$, revealing a behavior qualitatively similar to Fig. 1a. Also shown is the Hall resistivity ${\rho }_{xy}$ at $T=30\mathrm{m}\mathrm{K}$.Reuse & Permissions

Figure 3

Energy gap (${}^1\Delta$) of the $\nu =1$ QHS, measured as a function of $\Delta p$, at $p_{\mathrm{t}\mathrm{o}\mathrm{t}}=4.9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ for samples A ($d/l_B=1.45$) and B ($d/l_B=1.25$). Sample C ($p_{\mathrm{t}\mathrm{o}\mathrm{t}}=9.15\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ and $d/l_B=1.98$) does not exhibit a $\nu =1$ QH state in the range of imbalance studied; this is indicated by a zero energy gap. The dotted lines show the expected dependence of the separation (${\Delta }_{\mathrm{L}\mathrm{L}\mathrm{L}}$) between the lowest Landau levels of the two hole layers on $\Delta p$ for all three samples.Reuse & Permissions

Figure 4

Temperature dependence of ${\rho }_{xx}$ at $\nu \approx 1.1$, measured at several values of $\Delta p$ in sample B at $p_{\mathrm{t}\mathrm{o}\mathrm{t}}=4.9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$.Reuse & Permissions