  Thanks to the strong spin-orbit interaction (SOI), HgTe-based quantum wells
(QWs) exhibit very rich spin-related properties. But the full descriptions of
them are beyond the simple parabolic band models and conventional Rashba and
Dresselhaus SOI terms, as a result of the strong interband coupling of the
narrow gap band structures. Here, we develop a theoretical method to calculate
the circular photogalvanic effect (CPGE) in
Hg$_{0.3}$Cd$_{0.7}$Te/HgTe/Hg$_{0.3}$Cd$_{0.7}$Te quantum wells (HgTe QWs)
based on the realistic eight-band $\mathbf{k}\cdot\mathbf{p}$ model with
density matrix formalism. Our method could take account of the unusual band
structures and SOIs of HgTe QWs, therefore can be used to calculate the CPGE
currents in HgTe QWs with non-parabolic, Dirac-like and inverted energy
dispersions. The microscopic origin of CPGE and the interplay effect of
structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA) is also
investigated. In addition, this method is extended to study the pure spin
currents (PSCs) in HgTe QWs injected by linearly polarized light at normal
incidence. Our calculation results support the following findings: (i) In the
inverted phase regime, the energy dispersion of heavily inverted HgTe QWs could
be strongly distorted, lead to a significant enhancement of CPGE at a certain
range of energy spectrum. (ii) The interplay of SIA and BIA could lead to the
CPGE currents anisotropically dependent on the azimuth angle of oblique
incident light. (iii) The PSC $j_{y'}^{x'}$ ($x'\parallel[110]$ and
$y'\parallel[\bar{1}10]$) produced by [110]-linearly-polarized light could
change sign with HgTe QW transformed from normal phase to inverted phase. These
findings might be utilized in developing the HgTe-based infrared/terahertz
optoelectronic and spintronic devices.
