Effect of crossed static electric and magnetic fields on electronic transitions in a hollow cylindrical quantum wire

Electronic transition rates in a nanoshell are obtained as functions of crossed electric and magnetic fields in the dipole approximation. The main results of these investigations are rates of electronic transitions involving the lowest-order electron’s states, within the framework of Fermi’s golden rule. The system considered consists of a very long cylindrical core within which there are donor charges uniformly distributed throughout its volume. While the formulation applies to hollow cylinders of any material, the results shown are specific to GaAs cylinders. The core is then concentrically enveloped by a semiconductor specimen of uniform finite thickness. In addition, a homogeneous magnetic field is applied parallel to the axis of symmetry of the system of composite cylindrical nanostructures. The perturbing radiation field is taken to be that of circularly polarized light incident along the axis of the core. Of particular interest is that the axial applied magnetic field lifts the double degeneracies of electron sub-bands characterized by the same azimuthal quantum numbers (m), which differ only by sign. As a direct consequence of this Zeeman splitting, the transition rate is split into two branches corresponding to either of the ±|m| initial or final electron’s states. In general, resonance peaks are a typical signature of electronic transition rates whenever the electron’s sub-band energy separations exactly match the photon energy. Our results reveal that the inner radius significantly influences transition energies, offering means to tune the operational frequencies of nanostructures without altering their external dimensions, particularly advantageous when precise outer dimensions are required.