Zeeman splitting and g factor of heavy-hole excitons in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs quantum wells

Zeeman splittings have been investigated for n=1 heavy-hole excitons ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs strained-layer quantum wells at 1.8 K and at magnetic fields up to 6 T applied parallel to the growth axis (001). The sign and magnitude of the splitting to precision of ±2 μeV were obtained from the shift in the exciton photoluminescence line upon switching between right and left circularly polarized detection. Measurements have been made for well widths between 3 and 12 nm and for x values of 0.075 and 0.11. Linear field dependence is observed below 1.5 T giving exciton g factors. For higher fields in narrow wells the dependence becomes nonlinear. We have calculated the g factor using an eight-band k⋅p model and obtain satisfactory agreement with experiment by using the Luttinger parameter κ for ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As as a variable parameter. From this we obtain an empirical concentration dependence κ≊7.68x+1.1(1-x)-4.0x(1-x).