Impurity-related nonlinear optical properties in delta-doped quantum rings: Electric field effects

Using a variational procedure within the effective mass approximation, we have calculated the donor impurity binding energy for the ground (1s-like) and the excited (2pz-like) states as well as the impurity-related nonlinear optical absorption and relative changes in the refraction index in a GaAs single quantum ring with axial n-type delta-doping. The delta-like potential along the z-direction is an approximate model analytically described using a Lorentzian function with two parameters. Additionally we consider the application of an electric field along the z-direction. It is found that the changes in the geometry of the quantum ring, the change in the 2D impurity density of the delta-like doping, and different values of the electric field lead to a shifting of the resonant peaks of the optical responses spectrum.