The physics of the renormalization of the effective electron g factor by the confining potential in semiconductor nanostructures is theoretically investigated. The effective g factor for electrons in structures with interacting nanolayers, or coupled quantum wells (QWs), is obtained with an analytical and yet accurate multiband envelopefunction solution, based on the linear 8 × 8 k • p Kane model for the bulk band structure. Both longitudinal and transverse applied magnetic fields are considered and the g-factor anisotropy (i.e., the difference between the two field configurations) is analyzed over the entire space spanned by the two structure parameters: the thickness of the active layers and the thickness of the tunneling barrier separating them. Two-dimensional anisotropy maps are constructed for symmetric and asymmetric InGaAs coupled QWs, with InP tunneling barriers, that reproduce exactly known single-layer or QW results, in different limits. The effects of the structure inversion asymmetry on the mesoscopic g-factor renormalization are also discussed, in particular the negative anisotropies for thin-layer structures. Such multilayer structures form an excellent testing ground for the theory, and the analytical solution presented, which is perfectly consistent over the whole space of parameters, leads to helpful expressions and can guide further research on the mechanisms of this mesoscopic renormalization.

We investigate the quantum tunneling effects on the electron g factor and its main anisotropy in semiconductor double quantum wells (DQWs). With respect to single QWs, these structures introduce a new degree of freedom, given by the tunnel coupling parameter, and can be very helpful in the g-factor engineering. The eight-band effective-mass Hamiltonian for electrons in III-V double QWs and in the presence of an external magnetic field (applied both in the QW plane and along the growth direction) is solved for the g factor within first-order perturbation theory. We then calculate the g-factor anisotropy as a function of the QW width and the inter-well barrier length in typical AlGaAs/GaAs DQWs. The obtained results reproduce exactly the well-known single QW results in the corresponding limits, i.e. Lb=0 and very large, and explicitly show how the well-width dependence of the g-factor anisotropy changes with Lb, interpolating between these two limiting single QWs, with well width 2Lw and Lw respectively.

The inversion or sign change of the electron g-factor anisotropy in thin-layer semiconductor nanostructures is investigated theoretically and gauged for InGaAs asymmetric single and double quantum wells (QWs). The g-factor anisotropy in these 2D nanostructures is given by the difference between the longitudinal and transverse components; it is a fine sensor of the confining potential and in InGaAs structures it is determined by the Rashba spin-orbit coupling. In the presence of structure inversion asymmetry (SIA) the g-factor anisotropy is expected to invert at a critical well width. This effect can be useful technologically and is here analyzed in detail with InGaAs/InP asymmetric multi-layer structures. The g-factor anisotropy in these structures is calculated in a fine grid around the inversion point, using 8-band kp Kane model based envelope function theory for the nanostructure, and perturbation theory for the calculation of the effective g factor. It is shown that the anisotropy inversion can be seen only in asymmetric structures with very thin layers, near the limit of no bound states allowed, and corresponding to the electron being pushed out of the confining region. The inversion point, or critical well width for the g-factor anisotropy inversion in Insulator/InGaAs/ InP QWs is determined to be %4 nm. For double or coupled QWs it is found that the inversion can be observed only with very thin tunneling barriers around 1 nm wide.