of IQHE the fractional QHE (FQHE) was discovered [@Tsui1982]. Each of the discoveries — integer and fractional QHE — was awarded the Nobel prize. QHEs were extensively studied mostly in GaAs/(Ga,Al)As QWs and recently in 2D materials, such as graphene.

QHE is observed in 2-dimensional systems, where carrier movement in $z$-direction (perpendicular to the 2D plane) is quantized. From quantum mechanics it is known that confinement of electron motion in a potential well leads to quantization of energy eigenvalues $E_i$ (called subbands) in the growth direction, while the motion in the 2D plane remains unaffected. Further, we will consider only the lowest subband ($i=0$) to be occupied. Two phenomena lay in the basis of IQHE, namely Landau quantization of energy levels in a strong magnetic fields, and the disorder-induced localization. Application of a magnetic field splits the 2DEG’s energy levels into Landau levels (LLs) with energies: $E^N_c = \hbar\omega_c\left( N+\frac12\right)$. Here $\omega_c=eB/m^*$ is the cyclotron frequency, $\hbar$ — reduced Planck constant, $m^*$ — effective mass and $N$ is the LL index. Each LL is further split into two spin-resolved energy levels due to Zeeman effect. In wide-gap semiconductors the intrinsic Land[é]{} $g$-factor $g^*$ is relatively small (e.g., in ZnSe $g^*_{\text{ZnSe}}=+1.14$ 