Spin splitting in the electron subband of asymmetric ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells: The multiband envelope function approach

The dependence on carrier concentration of the anisotropic spin splitting of the lowest electron subband in asymmetrically doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells is determined. We employ the multiband envelope function approach based on 8×8 and $14\times 14\mathbf{k}\cdot \mathbf{p}$ Hamiltonians. Our self-consistent calculations yield results in quantitative agreement with experimental data obtained from inelastic light scattering.