Experimental results of the magnetotransport measurements (longitudinal magnetoresistance $R_{xx}$ and the Hall resistance $R_{xy}$) are presented over a wide interval of temperatures for several samples of ${\mathrm{Hg}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$ ($x\approx 0.13–0.15$) grown by MBE—thin layers (thickness about 100 nm) strained and not strained and thick ones with thickness about $1\mu \mathrm{m}$. An amazing temperature stability of the SdH-oscillation period and amplitude is observed in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behavior of the Hall resistance is registered in the same temperature interval. These peculiarities of the $R_{xx}$ and $R_{xy}$ for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS) [C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011)]. In the case of not strained layers it is assumed that the QHC on the TPSS (or on the resonant interface states) contributes also to the conductance of the bulk samples.

Temperature and gate voltage dependences of the 1/f noise in Hg_1−xCd_xTe and HgTe QW provide a strong argument for mobility fluctuations (δμ) as the dominant noise mechanism.