Orbital magnetism of three-dimensional quantum dots

We study the orbital magnetic response of three-dimensional quantum dots with parabolic confining potentials, emphasizing the roles of the longitudinal degrees of freedom parallel to an applied magnetic field. We find that the magnetic susceptibility as a function of the electron concentration is quite different depending on whether the system is isotropic or anisotropic with respect to the magnetic field; as the electron concentration varies, the response for the anisotropic case is para- or diamagnetic, while the one for the isotropic case is only diamagnetic.