Quantization of the Hall Conductance in a Three-Dimensional Layer

Abstract

Quantization of the Hall conductance is observed in epitaxial layers of heavily doped $n$-type GaAs with thickness $(\ensuremath{\approx}100\mathrm{nm})$ 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 $i\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,4,6$ 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 $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4\mathrm{K}$, ${G}_{\mathrm{xy}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}ie}^{2}/h$.