Highly nonlinear Zeeman splitting of excitons in semiconductor quantum wells

We have made a systematic investigation of the Zeeman splitting of n=1 heavy-hole excitons in a range of ${\mathrm{Al}}_{0.36}$${\mathrm{Ga}}_{0.64}$As/GaAs and ${\mathrm{In}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs (x=0.08 and 0.11) quantum wells at 1.8 K and in magnetic fields of up to 6 T applied along the growth axis (001). Calculations of splitting as a function of field were made using an eight-band K⋅P model which reproduce all the main features of the experimental data, including the sign, and give good quantitative agreement. The observed splittings are linear in low field (<1 T), but become nonlinear as field is increased. This behavior is attributed to a spin-dependent field-induced admixture between the light- and heavy-hole valence bands. For the GaAs/AlGaAs system agreement between experiment and theory requires a value for the Luttinger parameter κ in bulk GaAs close to 1.2 which is the generally accepted value, and rules out a lower value (0.7) which was proposed recently. From the theoretical fits to the ${\mathrm{In}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs Zeeman data we find that there is significant ``bowing'' of κ(x) which can be reproduced accurately using a perturbation theory relating the Luttinger κ and γ parameters, where ${\gamma }_{1,2,3}$ are obtained from experimentally determined light- and heavy-hole effective masses.