Tuning of the electron g factor in defect-free GaAs nanodisks

We theoretically study the impact of changes in surroundings on the electron ground-state effective $g$ factor in defect-free GaAs/AlGaAs nanodisks. To perform the study, we formulate and deploy a computational efficient full three-dimensional model to describe the effective $g$-factor tensor in semiconductor nano-objects of complex geometry and material content. This model is based on an effective $2\ifmmode\times\else\texttimes\fi{}2$ conduction-band Hamiltonian which includes the Rashba and Dresselhaus spin-orbit couplings. The description is suited to clarify the important question of the controllability of the electron effective $g$ factor in semiconductor nano-objects. The results of this theoretical study suggest that in the defect-free GaAs/AlGaAs nanodisks, the effective $g$ factor can be tuned within a wide range by proper design of the nanodisk environment. The $zz$ components of the electron effective $g$-factor tensor obtained in our simulation are in good agreement with some recent experimental observations.