Exciton, heavy-hole, and electron g factors in type-I GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

The magnetic g factor for n=1 heavy-hole–electron excitons in type-I GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells has been determined at 1.8 K as a function of well width (${\mathit{L}}_{\mathit{z}}$) from the Zeeman splitting of the luminescence line below 2 T. Combined with previously published g-factor measurements for electrons and heavy holes this gives a complete picture of the variation of the magnitudes and signs of the three g factors. The variation of electron g factor can be understood in terms of the nonparabolicity of the conduction band of GaAs using three-band k⋅p perturbation theory, but that of the hole and exciton g factors is not reproduced by existing theory, implying a well width dependence of the Luttinger parameters κ and q.