AC and DC conductivities in an $n$-GaAs/AlAs heterostructure with a wide quantum well in the integer quantum Hall effect regime

The direct-current (dc) $\sigma_{xx}^{dc}$ and alternating-current (ac) $\sigma^{ac}_{xx}=\sigma_1-i \sigma_2$ conductivities of a wide (46 nm) GaAs quantum well with the bilayer electron density distribution are measured. It is found that the magnetic field dependence of $\sigma_{xx}$ exhibits three sets of oscillations related to the transitions between Landau levels in symmetric and antisymmetric subbands and with the transitions occurring owing to the Zeeman splitting of these subbands. The analysis of the frequency dependence of the ac conductivity and the $\sigma_1/\sigma_2$ ratio demonstrates that the conductivity at the minima of oscillations is determined by the hopping mechanism.