Persistent currents in a thin hollow cylinder: The role of virtual channels

We investigate analytically and numerically the energy bands, persistent currents and the magnetic moment in a thin hollow cylinder in the presence of a magnetic field including the spin. Two different cases are considered systematically, an Aharonov-Bohm flux threading the hole of a cylinder and a magnetic field penetrating the whole cylinder. It is shown that the halving of the fundamental period of the magnetic moment can be attributed to the coupling of the azimuthal and paraxial electron motions caused by the impurity scattering. The influence of the virtual channels, resulting from evanescent states, on the energy bands and persistent currents is examined in detail. The virtual channels assure a continuous reconstruction of the energy bands immediately under the thresholds of the channels.