Evidence for Developing Fractional Quantum Hall States at Even Denominator $1/2$ and $1/4$ Fillings in Asymmetric Wide Quantum Wells

We report the observation of developing fractional quantum Hall states at Landau level filling factors $\nu =1/2$ and $1/4$ in electron systems confined to wide GaAs quantum wells with significantly asymmetric charge distributions. The very large electric subband separation and the highly asymmetric charge distribution at which we observe these quantum Hall states, together with the fact that they disappear when the charge distribution is made symmetric, suggest that these are one-component states, possibly described by the Moore-Read Pfaffian wave function.

Figure 1

(a),(b) Self-consistently calculated potential (black curves), total (solid blue and red curves), and the lowest subband charge distribution (dotted curves) for $n=1.72\times {10}^{11}{\mathrm{cm}}^{-2}$ electrons in a 55 nm-wide GaAs quantum well as the distribution is made asymmetric. (c) Fourier power spectra of the measured Shubnikov–de Haas oscillations for fixed $n=1.72\times {10}^{11}{\mathrm{cm}}^{-2}$ and different values of $\Delta n$ ranging from $-1.3$ to $10.4\times {10}^{10}{\mathrm{cm}}^{-2}$ (top to bottom trace) for sample $A$. The peak at 3.6 T corresponds to the total density in the WQW while the lower two peaks correspond to the two subband densities. (d),(e) Evolution of the magnetoresistance traces at $n=1.72\times {10}^{11}{\mathrm{cm}}^{-2}$ and for different $\Delta n$ as given on the left of each trace (in units of ${10}^{10}{\mathrm{cm}}^{-2}$). We observe a developing FQH state at $\nu =1/2$ for $\Delta n=7.8\times {10}^{10}{\mathrm{cm}}^{-2}$.

Figure 2

Evolution of magnetoresistance traces for sample $B$. The traces are shown for different total densities (indicated on the right) while the charge distribution is kept symmetric. As $n$ is decreased from 3.09 to $1.67\times {10}^{11}{\mathrm{cm}}^{-2}$, ${\Delta }_{\mathrm{SAS}}$ increases from 34 to 46 K. We observe a strong $\nu =1/2$ FQH state only at the highest $n$. Calculated charge distributions for two representative densities are also shown.

Figure 3

Magnetoresistance traces for sample $B$. The expected positions of $R_{xx}$ minima for the commonly observed, odd-denominator FQH states, as well as $\nu =1/2$ and $1/4$, are marked. Also shown are the positions of $R_{xx}$ minima expected for the imbalanced 2C states (530), (730), (752), and (753). For $R_{xy}$ traces, the expected positions of the plateaus for various FQH states are indicated by horizontal lines. Calculated total and lowest subband charge distributions are also shown.