Thermopower of Interacting GaAs Bilayer Hole Systems in the Reentrant Insulating Phase Near $\nu =1$

We report thermopower measurements of interacting GaAs bilayer hole systems. When the carrier densities in the two layers are equal, these systems exhibit a reentrant insulating phase near the quantum Hall state at total filling factor $\nu =1$. Our data show that, as the temperature is decreased, the thermopower diverges in the insulating phase. This behavior indicates the opening of an energy gap at low temperature, consistent with the formation of a pinned Wigner solid. We extract an energy gap and a Wigner solid melting phase diagram.

Figure 1

Upper panel: longitudinal resistivity ${\rho }_{xx}$ as a function of $B$ at the indicated temperatures for sample $A$ at a total density $p=5.1\times {10}^{11}\mathrm{c}{\mathrm{m}}^{-2}$. For the data in the figure, the densities of the individual layers are equal ($\Delta p=0$). Top inset: the $T$ dependence of ${\rho }_{xx}$ at $\nu =0.92$, 0.95, and 1.1. Bottom inset: a magnified view of the low-$B$ ${\rho }_{xx}$ trace at 30 mK. Lower panels: differential resistance in the insulating phase of sample $A$ as a function of the dc bias for $\nu =1.1$ (left panel) and 0.95 (right panel) at 30 mK.

Figure 2

$S_{xx}$ as a function of $B$ at four temperatures below 120 mK for sample $A$. Inset: $S_{xx}$ vs $B$ is displayed at $T=285$, 310, and 365 mK in the phonon-drag regime.

Figure 3

Top panel (sample $A$): $T$ dependence of $S_{xx}$ at different filling factors when the bilayer is balanced. Bottom panel (sample $B$): $T$ dependence of $S_{xx}$ at $\nu =1.14$ for balanced ($•$) and imbalanced ($\circ$) charge distributions. The dotted lines indicate various $T$ dependencies. The error bars are given by the noise of the lock-in amplifier, the magnitude of the applied thermal gradient, and the accuracy of the thermometers’ calibration.

Figure 4

Evolution of the melting temperature $T_m$ as a function of $\nu$ of the pinned, bilayer WS in sample $A$. The top axis shows the corresponding magnetic fields. Inset: $T_m$ is extracted from the $T$ dependence of $S_{xx}$ by assuming that the rise in $S_{xx}$ signals the melting of the WS.