G-factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

We analyze orbital effects of an in-plane magnetic field on the spin structure of states of a gated quantum dot based in a two-dimensional electron gas. Starting with a $k \cdot p$ Hamiltonian, we perturbatively calculate these effects for the conduction band of GaAs, up to the third power of the magnetic field. We quantify several corrections to the g-tensor and reveal their relative importance. We find that for typical parameters, the Rashba spin-orbit term and the isotropic term, $H_{43} \propto {\bf P}^2 {\bf B} \cdot \boldsymbol{\sigma}$, give the largest contributions in magnitude. The in-plane anisotropy of the g-factor is, on the other hand, dominated by the Dresselhaus spin-orbit term. At zero magnetic field, the total correction to the g-factor is typically 5-10% of its bulk value. In strong in-plane magnetic fields, the corrections are modified appreciably.