Zeeman-Stark problem in a two-dimensional disk

Under a perpendicular magnetic field, electrons in two-dimensional disks occupy quantum-confined Landau levels. By analyzing the electric polarizability of such states, we reveal an extreme sensitivity to confinement. Hence, an exponential increase with magnetic field or disk size is found and ascribed to the linear Zeeman effect. In contrast, if the balance between linear and quadratic Zeeman terms is slightly reduced, due to, e.g., addition of a nonmagnetic parabolic potential, the polarizability varies nonmonotonically with field strength and eventually vanishes. The analysis is based on a compact exact expression for the polarizability valid for arbitrary magnetic field, disk size, and linear Zeeman strength.