Fractional quantum Hall effect at low temperatures

Abstract

We report a systematic study of the $\frac{2}{3}$ fractional quantum Hall effect at low temperatures (65-770 mK) for a GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ sample of very high mobility (${10}^6$ ${\mathrm{cm}}^2$/V sec). We find the $\frac{2}{3}$ Hall plateau to be accurately quantized. The diagonal and Hall resistivities are observed to be activated at each given filling factor $\nu =\frac{\mathrm{nh}}{\mathrm{eB}}$ around $\frac{2}{3}$. The activation energy has a maximum value, ${\Delta }_{max}$, at $\nu =\frac{2}{3}$ and decreases to each side as $\nu$ moves away. By varying the sample mobility and density simultaneously with a backgate bias, we find ${\Delta }_{max}$ strongly mobility and magnetic field dependent.