We study the electronic states of core multi-shell semiconductor nanowires, including the effect of strong magnetic fields. We show that the multi-shell overgrowth of a free-standing nanowire, together with the prismatic symmetry of the substrate, ma
y induce quantum confinement of carriers in a set of quasi-1D quantum channels corresponding to the nanowire edges. Localization and inter-channel tunnel coupling are controlled by the curvature at the edges and the diameter of the underlying nanowire. We also show that a magnetic field may induce either Aharonov-Bohm oscillations of the energy levels in the axial configuration, or a dimensional transition of the quantum states from quasi-1D to Landau levels for fields normal to the axis. Explicit predictions are given for nanostructures based on GaAs, InAs, and InGaN with different symmetries.
We compute the single-particle states of a two-dimensional electron gas confined to the surface of a cylinder immersed in a magnetic field. The envelope-function equation has been solved exactly for both an homogeneous and a periodically modulated ma
gnetic field perpendicular to the cylinder axis. The nature and energy dispersion of the quantum states reflects the interplay between different lengthscales, namely, the cylinder diameter, the magnetic length, and, possibly, the wavelength of the field modulation. We show that a transverse homogeneous magnetic field drives carrier states from a quasi-2D (cylindrical) regime to a quasi-1D regime where carriers form channels along the cylinder surface. Furthermore, a magnetic field which is periodically modulated along the cylinder axis may confine the carriers to tunnel-coupled stripes, rings or dots on the cylinder surface, depending on the ratio between the the field periodicity and the cylinder radius. Results in different regimes are traced to either incipient Landau levels formation or Aharonov-Bohm behaviour.
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the well-known geomet
ric potential. The electric and magnetic fields are included via the four-potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, the Hamiltonian for the cylinder, sphere and torus are analytically derived.
