Effects of an In-plane Magnetic Field on the Electron g-factor in a 2DEG Quantum Dot

We investigate the interplay between an in-plane external magnetic field and the spin-orbit interaction in a quasi-two-dimensional electron gas (2DEG) quantum dot formed in the GaAs/AlGaAs heterostructure. In the presence of the applied in-plane magnetic field and out-of-plane electric field, the spin-orbit interaction can alter the spin states of the electron in the 2DEG quantum dot. We quantify such effect by computing the corrections to the electron g-factor in the lowest subband of the dot confinement potential. Using the third-order Lowdin perturbation theory, we find that the spin-orbit interaction can lead to significant corrections to the g-factor in a finite magnetic field, with the triangular confinement potential perpendicular to the 2DEG and bi-harmonic confinement potential in the 2DEG plane. We present the anisotropic g-factor corrections up to third order in the magnetic flux, as a function of the magnitude and direction of the magnetic field, as well as the dot orientation with respect to the crystallographic axes.