Magnetotransport in double quantum well with inverted energy spectrum: HgTe/CdHgTe

We present an experimental study of the double-quantum-well (DQW) system made of two-dimensional layers with inverted energy band spectrum: HgTe. The magnetotransport reveals a considerably larger overlap of the conduction and valence subbands than in known HgTe single quantum wells (QW), which may be regulated here by an applied gate voltage ${V}_g$. This large overlap manifests itself in a much higher critical field ${B}_c$ separating the range above it with a plain behavior of the Hall magnetoresistance ${\ensuremath{\rho}}_xy(B)$, where the quantum peculiarities shift linearly with ${V}_g$, and the range below with a complicated behavior. In the latter case, specific structures in ${\ensuremath{\rho}}_xy(B)$ are formed like a double-$N$-shaped ${\ensuremath{\rho}}_xy(B)$, reentrant sign-alternating quantum Hall effect with transitions into a zero-filling-factor state, etc., which are clearly manifested here due to better magnetic quantization at high fields, as compared to the features seen earlier in a single HgTe QW. The coexisting electrons and holes were found in the whole investigated range of positive and negative ${V}_g$ as revealed (i) from fits to the low-field $N$-shaped ${\ensuremath{\rho}}_xy(B)$, (ii) from the Fourier analysis of oscillations in ${\ensuremath{\rho}}_xx(B)$, and (iii) from a specific behavior of ${\ensuremath{\rho}}_xy(B)$ at high positive ${V}_g$. A peculiar feature here is that the found electron density $n$ remains almost constant in the whole range of investigated ${V}_g$ while the hole density $p$ drops down from the value a factor of 6 larger than $n$ at extreme negative ${V}_g$ to almost zero at extreme positive ${V}_g$ passing through the charge-neutrality point. We show that this difference between $n$ and $p$ stems from an order of magnitude larger density of states for holes in the lateral valence subband maxima than for electrons in the conduction subband minimum. We analyze our observations on the basis of a calculated picture of magnetic levels in a DQW and suggest that their specificity is due to (i) a nonmonotonic course of the valence subband magnetic levels and an oscillating behavior of the valence subband top versus field due to lateral maxima in the energy spectrum, (ii) a reduced gap between the lowest-electron and the highest-hole magnetic levels where the electron- and hole-type localized states are superposed, and (iii) a possible formation of the interlayer electron-hole excitons.