  By means the envelope function approximation, 8-band Kane model and a
finite-difference scheme with the coordinate space discretization, we
numerically performed calculations of the spin-orbit coupling parameters for 2D
electron gas confined in both symmetric and asymmetric [0 0 1] quantum wells
based on zinc-blende III-V semiconductors. Influence of the quantum well band
parameters and width as well as the magnitude of the external electric field
applied along the growth direction on the Dresselhaus and Rashba spin-orbit
coupling parameters is investigated. It has been found that in the symmetric
InGaAs/GaAs quantum wells linear-in-momentum spin-orbit coupling disappears for
the third electron subband at certain values of well width and the indium
content. It is also shown that in asymmetric InGaAs/GaAs structures the
spin-orbit coupling parameters can be equal at a certain electric field that is
the condition for the realization of the SU(2) spin symmetry and formation of
persistent spin helices. Besides, we calculated the spin-orbit coupling in the
persistent spin helix regime as a function of the well width, indium content
and external field. The proposed approach for the calculation of the spin-orbit
coupling parameters can be applied to other 2D structures with the spin-orbit
coupling.
