Mesoscopic spin-orbit effect in the semiconductor nanostructure electrongfactor

Abstract

The renormalization of the electron $g$ factor by the confining potential in semiconductor nanostructures is considered. A new effective $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian for the electronic states in III--V semiconductor nanostructures in the presence of an external magnetic field is introduced. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. It is then solved analytically for the electron effective $g$ factor in symmetric quantum wells (${g}_{\mathrm{QW}}^{*}$). Comparison with different spin quantum beat measurements in GaAs and InGaAs structures demonstrates the accuracy and utility of the theory. The quantum size effects in ${g}_{\mathrm{QW}}^{*}$ are easily understood and its anisotropy $\ensuremath{\Delta}{g}_{\mathrm{QW}}^{*}$ (i.e., the difference between the in-plane and perpendicular configurations) is shown to be given by a mesoscopic spin-orbit effect having the same origin as the Rashba one.