Features of magnetotransport in a $\mathrm{HgTe/CdHgTe}$ double quantum well with an intermediate degree of band inversion

A stepwise behavior of the Hall magnetoresistance $\rho_{yx}(B)$ with an almost vertical increase around zero and a further trend close to $h/e^2$ has been revealed in a double quantum well consisting of two $8.5$-nm-thick HgTe layers separated by a $3$-nm barrier. The band structure of the double quantum well is characterized by a sharp maximum in the center of the Brillouin zone, which is close in energy to the lateral maximum. The observed sharp increase in $\rho_{yx}(B)$ near zero is consistent with a vanishingly low concentration of light holes at this maximum, but the further almost horizontal behavior is inconsistent with the classical description of $\rho_{yx}(B)$ for a high concentration of low-mobility holes at the lateral maximum and implies quantum effects. A high sensitivity of the observed behavior of $\rho_{yx}(B)$ to external fields (electric field perpendicular to the layers and a parallel magnetic field) has been detected in agreement with change in fine balance of the positions of the central and lateral maxima. It has been shown that this property occurs because the double quantum well has a specific dipole moment distinguishing it from the single quantum well with similar features of the band structure; consequently, the response of the single quantum well should be much weaker.