Quantization of the Hall Conductance in a Three-Dimensional Layer

Quantization of the Hall conductance is observed in epitaxial layers of heavily doped $n$-type GaAs with thickness $\left(\approx 100\mathrm{nm}\right)$ larger than both the screening length and the mean free path of the conduction electrons. Therefore, the single-particle spectrum of the electrons is three dimensional. Analogous to the quantum Hall effect in two-dimensional systems, the magnetic field $B$ dependence of the Hall conductance $G_{\mathrm{xy}}$ shows, below 1 K, steps at quantized values ${\mathrm{ie}}^2/h$ for $i=2,4,6\mathrm{}$ together with pronounced minima in the transverse conductance $G_{\mathrm{xx}}$. The minima in $G_{\mathrm{xx}}$ and $|{\mathrm{dG}}_{\mathrm{xy}}/\mathrm{dB}|$ appear in magnetic fields where, at $T=4\mathrm{}\mathrm{K}$, $G_{\mathrm{xy}}{=ie}^2/h$.