We derive the Schrödinger equation for a spinless charged particle constrained to move on a curved surface in the presence of an electric and magnetic field. The particle is confined on the surface using a thin-layer procedure, which gives rise to the well-known geometric 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, we derive an analytic form of the Hamiltonian for spherical, cylindrical, and toroidal surfaces.

We study the electronic states of core multishell semiconductor nanowires, including the effect of strong magnetic fields. We show that the multishell overgrowth of a free-standing nanowire, together with the prismatic symmetry of the substrate, may induce quantum confinement of carriers in a set of quasi-1D quantum channels corresponding to the nanowire edges. Localization and interchannel 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.

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Quantum transmission spectra of a twisted electron waveguide expose the coupling between traveling andquasibound states. Through a direct numerical solution of the open-boundary Schroedinger equation, we singleout the effects of the twist and show how the presence of a localized state leads to a Breit-Wigner or a Fanoresonance in the transmission.We also find that the energy of quasibound states is increased by the twist, despitethe constant section area along the waveguide. While the mixing of different transmission channels is expectedto reduce the conductance, the shift of localized levels into the traveling-states energy range can reduce theirdetrimental effects on coherent transport