HYDROGENIC IMPURITY IN A QUANTUM WIRE: EFFECT OF DIFFERENT MASSES OF WIRE AND BARRIER

Abstract

A variational calculation is given within the effective mass approximation of the binding energy of a hydrogenic donor impurity located on the axis of an infinitely long circular quantum well wire. A uniform magnetic field is applied along the axis of the wire. The different effective masses of the wire and the barrier are taken into consideration. This has not been done hitherto in the presence of the magnetic field. New analytical expressions for the electron energy levels and the binding energies of the hydrogenic impurity in the ground and the first four excited states have been derived. Moreover, the form of the binding energy reported in earlier works in the special case of zero magnetic field has been amended. A new form of the trial wavefunction has also been introduced. It has the advantage of satisfying the required boundary conditions in the case of different masses of the wire and barrier, and thus it resembles the exact solution in this respect. The new form of the trial wavefunction has been applied to the case of the ground state. It has improved the results of binding energy considerably as they tend to approach the exact solution from below.