Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field

Using the finite element method, we investigate the lowest and first few excited state energies in a two- dimensional GaAs quantum ring （QR） with a hydrogenic donor impurity and effective mass approximation under a uniform magnetic field perpendicular to the ring plane. We study in detail the dependence of the energy spectrum with different angular momentum on the inner radius, the outer radius and width of the QR, the magnetic field and impurity position. The results reveal that the electron energies increase with the inner radius while decrease with the outer radius and width of the QR; for a fixed ring, the magnetic field induces the increase of the electron energies. Moreover, the existence of impurity reduces energy levels, and the energy levels depend highly on the impurity position, which decreases as the impurity is far away from the center of the QR. Also, the dependence of the angular momentum on the energy spectrum is analyzed in detail.