Observation of Reentrant Integer Quantum Hall States in the Lowest Landau Level

Measurements on very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal a close competition between the electron liquid and solid phases near the Landau level filling factor $\nu =1$. As the density is raised, the fractional quantum Hall liquid at $\nu =4/5$ suddenly disappears at a well-width dependent critical density, and then reappears at higher densities with insulating phases on its flanks. These insulating phases exhibit reentrant $\nu =1$ integer quantum Hall effects and signal the formation of electron Wigner crystal states. Qualitatively similar phenomena are seen near $\nu =6/5$.

Figure 1

$R_{xx}$ and $R_{xy}$ vs $1/\nu$ traces at $T=30\mathrm{mK}$ for a 42-nm-wide GaAs QW at two densities: (a) $n=1.78$, and (b) $2.46\times {10}^{11}{\mathrm{cm}}^{-2}$. In (b), the RIQHE phases observed on two sides of $\nu =4/5$ are marked by arrows.

Figure 2

Waterfall plots of $R_{xx}$ and $R_{xy}$ vs $1/\nu$ for the 42-nm-wide QW as $n$ is changed from 1.78 to $3.41\times {10}^{11}{\mathrm{cm}}^{-2}$. Traces are shifted vertically for clarity. The down arrows mark the development of RIQHE phases near $1/\nu =1.20$ as $n$ is raised from 2.05 to $2.61\times {10}^{11}{\mathrm{cm}}^{-2}$, and near $1/\nu =0.86$ as $n$ is further increased. The up arrows in the top panel mark the development of similar, albeit weaker, RIQHE phases near $1/\nu =1.28$ and 0.83. The yellow band marks the range $0.85\le \nu \le 1.15$ ($0.87>1/\nu >1.18$); see text.

Figure 3

(a) Evolution of $R_{xx}$ and $R_{xy}$ with temperature for the 42-nm QW at $n=2.46\times {10}^{11}{\mathrm{cm}}^{-2}$. (b) Waterfall plots of $R_{xx}$ and $R_{xy}$ vs $1/\nu$ for the 31-nm QW sample, showing how the RIQHE phase near $1/\nu =1.20$ starts to develop as $n$ is raised from 3.05 to $3.48\times {10}^{11}{\mathrm{cm}}^{-2}$. Data are shifted vertically for clarity. The inset shows the $T$ dependence of the RIQHE at $n=3.33\times {10}^{11}{\mathrm{cm}}^{-2}$. (c) $R_{xx}$ and $R_{xy}$ traces for the 44-nm QW at $n=3.83\times {10}^{11}{\mathrm{cm}}^{-2}$ displaying a RIQHE phase at $1/\nu =1.28$. (d) Dependence of the critical density $n_c$ above which the RIQHE near $\nu =4/5$ sets in on QW width $W$. The insets show the self-consistently calculated charge distribution and potential for the 31- and 42-nm QWs at $n_c$.