## 2 Samples and Experiment  
### Wafers' Description and Characterization  
Cadmium Telluride QWs with CdMgTe barriers were grown by molecular beam epitaxy on a semi-insulating GaAs substrate. In the case of wafer A Figure 1, top), a 3 \(\upmu\)m-thick CdTe and a 3 \(\upmu\)m-thick CdMgTe layers were grown followed by 5 repetitions of a short period superlattice (SPSL; each period of SPSL consisted of 10 repetitions of 4 monolayers of CdTe and 4 monolayers of CdMgTeseparated by a 100 nm-thick CdMgTe spacer). Then, a 20 nm-thick CdTe QW was grown and the growth ended with a 80 nm-thick CdTeMg layer. In the case of wafer B Figure 1, bottom), the buffer layer consisted of a 2.2 \(\upmu\)m-thick CdTe, a 1.5 \(\upmu\)m-thick CdMgTe layer and 5 repetitions of SPSL (each period of SPSL consisted of 10 repetitions of 2 monolayers of CdTe and 2 monolayers of CdMgTe separated by a 52 nm-thick CdMgTe spacer). Next, two 10.5 nm-thick modulation doped CdTe quantum wells (QWs) separated by 44 nm-thick CdMgTe barrier were grown. The growth was finished with a 45 nm-thick CdMgTe cap layer. The Magnesium content in the barriers was equal to 21% and 26% in the wafers A and B, respectively. Modulation doping with Iodine donors resulted in appearence of a 2 DEG in the wells.  
Magnetotransport measurements showed that the concentration \(n_{s}\) of electrons in the wafer A (one QW) is equal to about \(3.3\times 10^{11}\) cm\({}^{-2}\). In the case of wafer B (two QWs), the concentration \(n_{s}\) in each QW is equal to \(4.7\times 10^{11}\) cm\({}^{-2}\) which means that the total concentration of 2 DEG in samples from the wafer B is almost 3 times higher than in the wafer A. Mobility of electrons in both wafers was estimated at the level of about \(3.5\times 10^{5}\) cm\({}^{2}\)/Vs at liquid helium temperatures.  
Terahertz magnetospectroscopy measurements were carried out with the samples placed in a variable temperature insert in the center of a superconducting coil (a complet system from Cryogenic Ltd., London, UK). The temperature of the sample was equal to 2 K and the sample was in a direct contact with superfluid helium. The end of an optical fiber was attached close to the sample which allowed us to illuminate the sample with white light from a halogen lamp. A molecular laser (FIRL-100, Edinburgh Instrument LTd., Livingston, UK) working on methanol vapour) optically pumped with a CO\({}_{2}\) laser was used as a source of THz radiation. We used the laser lines with photon's wavelength equal to 96 \(\upmu\)m, 118.8 \(\upmu\)m, 164 \(\upmu\)m and 186 \(\upmu\)m (corresponding to 3.11 THz, 2.52 THz, 1.82 THz and 1.61 THz, respectively). Radiation was guided to the sample with an oversized wave guide (a stainless steel tube, diameter 12 mm) which ended with a copper cone to focalize radiation on the sample. A signal transmitted through the sample was detected with a home-made bolometer (in the form of a mechanically thinned carbon Alan-Bradley resistor) and registered with a lock-in technique. The signal was registered as a function of magnetic field. A dependence of the transmitted signal on \(B\) is named \"a spectrum\" in this paper. The spectra were normalized to the power of the laser beam (registered with a pyroelectric detector). This normalization reduced the noise and long-term instability of the laser power in a single scan of \(B\) which typically lasted about 20 min. However, the experimental set-up did not allow us to measure the power of radiation incident on the sample. For this reason  
Figure 1: SEM photographs of the layered structure of the wafer A with one QW (**top**) and the wafer B with two QWs (**bottom**).  
and for a better comparison of different spectra, after normalization to the read out of the pyroelectric detector, the spectra were normalized to coincide at low \(B\).