Hydrogenic impurities in cylindrical quantum wires in the presence of a magnetic field

A systematic study of the binding energy of the ground state of a hydrogenic donor in a cylindrical quantum wire is calculated in the presence of a uniform magnetic field applied parallel to the wire axis. Calculations are performed within the effective mass approximation using the variation procedure considering both infinite and finite potentials. We assume that the impurity ion is located at the axis of the wire. The quantum wire is assumed to a cylinder of GaAs material surrounded by Ga1-xAsxAs. The binding energy is calculated as a function of the radius of the wire and the applied magnetic field. For the infinite potential well model, the binding energy continues to increase as the radius of the wire decreases whereas in the finite case, the binding energy reaches a peak value as the wire radius decreases to a value characteristic of the cladding. For a given value of the magnetic field, the binding energy is found to be larger than the zero field case. The results are compared with available data in the literature.