[@Cavenett1981]; in CdTe $g^*_{\text{CdTe}}=-1.6$ [@Simmonds1982]) so the Zeeman splitting $E_z$ of LL is generally much smaller than the cyclotron gap. In a magnetic field $B$ 2DEG will split into the following spin-resolved LLs: $$E_{N,\uparrow,\downarrow} = E^N_c + E_z = \hbar\omega_c\left(N+\frac12\right) \pm \frac12g^*\mu_BB,
\label{eqLL_spin}$$ where $E^N_c$ is the cyclotron energy, $E_z$ is the Zeeman energy and $\pm\frac12$ stands for spin orientation $\uparrow$ and $\downarrow$.

In real samples, these discrete LLs are smeared into bands due to both thermal broadening and scattering. Thus, the resulting density of states in a high magnetic field is split into a sequence of broadened $\delta$-peaks at energy values corresponding to spin-split LLs. The states close to the center of the LL band are extended, while the states in the tails of LLs are localized and do not contribute to transport. Only the extended states can carry current at zero temperature. When these extended states overlap the Hall resistance $R_{xy}$ is not quantized and the longitudinal resistance $R_{xx}$ exhibits SdH oscillations due to the oscillating density of states. With increasing of a magnetic field this overlap diminishes. If $E_F$ lays between LL bands, $R_{xy}$ exhibits plateaus at the quantized values $\frac{h}{\nu e^2}$, where $\nu$ (called filling factor) 