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 Al0.36Ga0.64As/GaAs and InxGa1-xAs/ GaAs (x=0.08 and 0.11) quantum wells at 1.8 K and in magnetic fields o f up to 6 T applied along the growth axis (001). Calculations of split ting as a function of field were made using an eight-band K . P model which reproduce all the main features of the experimental data, includ ing the sign, and give good quantitative agreement. The observed split tings are Linear in low field (<1 T), but become nonlinear as field is increased. This behavior is attributed to a spin-dependent field-indu ced 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 kappa in bulk GaAs close to 1.2 whi ch is the generally accepted value, and rules out a lower value (0.7) which was proposed recently. From the theoretical fits to the InxGa1-x As/GaAs Zeeman data we find that there is significant ''bowing'' of ka ppa(x) which can be reproduced accurately using a perturbation theory relating the Luttinger kappa and gamma parameters, where gamma(1,2,3) are obtained from experimentally determined light- and heavy-hole effe ctive masses.