Valence band structure of $\mathrm{HgTe}/{\mathrm{Hg}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}$ single quantum wells

Properties of the valence-band structure of modulation-doped type-III $\mathrm{HgTe}/{\mathrm{Hg}}_{1-x}{\mathrm{Cd}}_x\mathrm{Te}\mathrm{}\left(001\right)\mathrm{}$ quantum wells (QW’s) have been studied by means of magneto-transport experiments and self-consistent Hartree calculations using the full $8\times 8\mathit{k}\cdot \mathit{p}$ Hamiltonian in the envelope-function approximation. A metallic top gate was used in order to investigate the band structure by varying the hole concentration or the Fermi energy. This resulted in direct experimental evidence of an indirect band gap in a quantum well with an inverted band structure. The Kramers degeneracy for finite k is removed, and only one spin-orbit split valence subband is occupied due to the indirect band structure. The fourfold symmetry of the $H2\mathrm{}$ valence band at finite values of ${\mathit{k}}_{\Vert }$ is also reflected in a QW with a normal band structure, whose $H1\mathrm{}$ valence band has four occupied secondary maxima at finite values of ${\mathit{k}}_{\Vert }$ in addition to the central maximum.