Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well

We report the observation of an even-denominator fractional quantum Hall state at $\nu =1/4$ in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of $n_e=2.55\times {10}^{11}{\mathrm{cm}}^{-2}$. We have performed transport measurements at $T\sim 35\mathrm{mK}$ in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at $\nu =1/4$. Upon tilting the sample to an angle of $\theta =20.3°$ a clear fractional quantum Hall state emerges at $\nu =1/4$ with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.

Figure 1

$R_{xx}$ and $R_{xy}$ as a function of the perpendicular component of the magnetic field $B_{\perp }$ for $\theta =0°$ and 20.3° at $T\simeq 35\mathrm{mK}$. Many of the odd-denominator FQH states are labeled. The filling factors $\nu =1/2$ and $\nu =1/4$ are also marked. The horizontal lines at $R_{xy}=2h/e^2$, $3h/e^2$, and $3.9h/e^2$ highlight the plateaus at those values. In the inset in the upper left corner we show the zero-field, self-consistently calculated results of the electronic potential (solid line) and the electron distribution across the well (dashed line).

Figure 2

(a) $R_{xy}$ and (b) $R_{xx}$ as a function of $B_{\perp }$ near $\nu =1/4$ for $\theta =0°$ and 20.3°. The odd-denominator states and the FQH state at $\nu =1/4$ are indicated by arrows. The expected values of the plateaus in $R_{xy}$ are marked with horizontal lines. The actual value of the plateau $R_{xy}=3.9h/e^2$ at $\nu =1/4$ is also shown.

Figure 3

$R_{xx}$ near $\nu =1/2$ and $\nu =1/4$ with $\theta =0°$ for (a), (c) $n_e=2.55\times {10}^{11}{\mathrm{cm}}^{-2}$ and (b), (d) $n_e=2.65\times {10}^{11}{\mathrm{cm}}^{-2}$. In the case of $\nu =1/2$ the strength of the FQH state is increased, while for $\nu =1/4$ no FQH state is observed in either case.