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

We report a calculation of the binding energy of the ground state of a hydrogenic donor in a quantum wire in the presence of a uniform magnetic field applied parallel to the wire axis. We assume that the impurity ion is located at the axis of the wire. The quantum wire is assumed to be a cylinder of GaAs material surrounded by ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As. The calculations have been performed by using suitable variational wave functions for infinite and finite confinement potentials. For a given value of the magnetic field, the binding energy is found to be larger than the zero-field case.