Fractional quantum Hall effect in a two-dimensional hole system

Abstract

We have studied the fractional quantization of the Hall resistance at 0.51 K in two-dimensional hole systems formed at $p^{+}:{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$-GaAs interfaces with mobilities as high as 8.0 × ${10}^4$ ${\mathrm{cm}}^2$/Vs at 4 K. In addition to the Hall quantization for a fractional filling factor $\nu =\frac{2}{3}$, we report for the first time the observation of an almost fully developed Hall plateau at $\nu =\frac{3}{5}$ and the existence of weak but distinct structure in the magnetoresistance for $\nu =\frac{3}{7} \mathrm{and} \frac{6}{5}$. Similarly, magnetoresistance minima occurred at $\nu =\frac{5}{3}, \frac{4}{3}, \frac{2}{3}, \frac{3}{5}, \mathrm{and} \frac{2}{5}$. In contrast with two-dimensional electron systems, conspicuously absent was any magnetoresistance feature in the vicinity of $\nu =\frac{4}{5}$.