Enhancement of spin splitting due to spatial confinement in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum dots

The splitting between the ${\mathrm{\sigma }}^{+}$ and the ${\mathrm{\sigma }}^{\mathrm{-}}$ polarized spectral lines that arise from the ground-state transitions of ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum dots has been investigated by photoluminescence studies in magnetic fields up to B=8 T. We find that the difference in energy between these two lines increases drastically with decreasing dot diameter. This increase is attributed to the enhancement of the g factor of the hole ground state with zero angular momentum, which obtains admixtures of hole states with nonzero orbital angular momenta. The admixtures originate from the strong spin-orbit interaction in the valence band that is increased by the spatial confinement.