Electric field dependence of the electron g-factor for a Si donor in bulk GaAs

Modulation of the electron g-factor by an applied electric field may be used to coherently manipulate spins for quantum information processing. We present numerical calculations of the electric field dependence of the $g$-factor of an electron bound to a silicon donor in bulk GaAs. The calculations were carried out using 8-band $k.p$ theory in the envelope function approximation, which is implemented using finite differences on a real-space grid. The binding energy of the Si impurity in GaAs was fit to experimental data by adding a central cell correction to the donor site. Electrically modulating the impurity's $g$-factor is possible as the electric field modifies the binding energy for the Si donor. In our calculations, it is seen that the variation in $g$ is nearly quadratic as a function of electric field (up to 0.2 mV/nm) and for $E=0$, ${d^2g} / {dE^2}=1.2~ \rm (mV/nm)^{-2}$. The largest variation in $g$ is obtained when the applied magnetic field and electric fields are in the same direction. The proposed scheme provides a realizable alternative to quantum information processing using quantum dots.