Electron States in Quasi-One-Dimensional Structures; Azimuthal Applied Magnetic Field

Abstract

The energy spectrum of a single electron confined in a cylindrical quantum wire is determined within the effective-mass approximation as a function of the azimuthal applied magnetic field. The magnetic field varies linearly with the radial distance across the wire thickness. Unlike in the case of a cylinder in a parallel magnetic field, the azimuthally directed magnetic field preserves the double degeneracy of the non-zero azithumal quantum number (m) states. In this case, the azimuthal magnetic field instead lifts the double degeneracy of the non-zero axial wavenumber (kz) states. A further analysis is the evaluations of the oscillator strengths for optical transitions involving the lowest-order energy subbands of the electron, within the dipole approximation. The radiation field with clear-cut selection rules for optical transitions is that of circularly polarized, incident along the axis of the cylinder. It emerges that the triple degeneracy of the oscillator strengths, when kz ≠ 0, is lifted by the magnetic field. In terms of the arising branches for the oscillator strengths, the transitions for which kz < 0 are enhanced the most by the azimuthal applied magnetic field.