= Solution
The <integer quantum Hall effect> requires a conducting <two-dimensional electron gas> with well-resolved <Landau levels>. In the simple parabolic-band model their orbital spacing is
$$
\hbar\omega_c=\frac{\hbar eB}{m^*}.
$$
Low <temperature> and sufficiently low disorder broadening are needed so that $k_BT$ and the relevant level width $\Gamma$ are small compared with this spacing. A high-mobility sample with $\omega_c\tau\gg1$ is therefore useful.
Some disorder has a constructive role: localized states between extended Landau-level states allow the <Fermi energy> to move through a range of carrier populations while the transport response stays on a plateau. The longitudinal response is then very small and the transverse response is quantized. Whether odd or only even integer plateaux are resolved also depends on whether spin splitting is resolved.
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