Correlated States of Electrons in Wide Quantum Wells at Low Fillings: The Role of Charge Distribution Symmetry

Magnetotransport measurements on electrons confined to a 57-nm-wide, GaAs quantum well reveal that the correlated electron states at low Landau level fillings ($\nu$) display a remarkable dependence on the symmetry of the electron charge distribution. At a density of $1.93\times {10}^{11}{\mathrm{cm}}^{-2}$, a developing fractional quantum Hall state is observed at the even-denominator filling $\nu =1/4$ when the distribution is symmetric, but it quickly vanishes when the distribution is made asymmetric. At lower densities, as we make the charge distribution asymmetric, we observe a rapid strengthening of the insulating phases that surround the $\nu =1/5$ fractional quantum Hall state.

Figure 1

(a) Evolution of FQHSs for a 57-nm-wide GaAs quantum well with $n=1.93\times {10}^{11}{\mathrm{cm}}^{-2}$ as the charge distribution is made asymmetric. (b),(c) Self consistently calculated electron distributions and potentials for $\Delta n=0$ and $\Delta n=3.3\times {10}^{10}{\mathrm{cm}}^{-2}$. (d) Experimentally measured (squares) and calculated (curve) subband energy difference (${\Delta }_{01}$) vs $\Delta n$.

Figure 2

${\rho }_{xx}$ plotted vs inverse filling factor for different densities. Minima at $\nu =1/2$ and $1/4$ get weaker with lowering the density. The inset shows the calculated charge distribution at $n=1.93\times {10}^{11}{\mathrm{cm}}^{-2}$ (red curve) and $n=1.50\times {10}^{11}{\mathrm{cm}}^{-2}$ (black curve).

Figure 3

Hall resistivity and its derivative are plotted as a function of magnetic field.

Figure 4

(a) Resistivity vs $B$ at $n=1.50\times {10}^{11}{\mathrm{cm}}^{-2}$ for different $\Delta n$. The upper traces (left scale) are expansions of the lower traces (right scale). (b),(c) Temperature dependence of ${\rho }_{xx}$ for $\Delta n=0$ and $\Delta n=6.3\times {10}^{10}{\mathrm{cm}}^{-2}$.