Zero-field spin splitting in an invertedIn0.53Ga0.47As/In0.52Al0.48Asheterostructure: Band nonparabolicity influence and the subband dependence

A gated inverted ${\mathrm{In}}_{0.52}{\mathrm{Al}}_{0.48}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.53}{\mathrm{Ga}}_{0.47}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ quantum well is studied via magnetotransport. By analyzing the gate-voltage-dependent beating pattern observed in the Shubnikov--de Haas oscillation, we determine the gate voltage (or electron concentration) dependence of the spin-orbit coupling parameter \ensuremath{\alpha}. Our experimental data and its analysis show that the band nonparabolicity effect cannot be neglected. For electron concentrations above $2\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2},$ it causes a reduction of \ensuremath{\alpha} up to 25%. We report the \ensuremath{\alpha} value for the second subband.