  The gap oscillations caused by a magnetic flux penetrating a carbon nanotube
represent one of the most spectacular observation of the Aharonov-Bohm effect
at the nano--scale. Our understanding of this effect is, however, based on the
assumption that the electrons are strictly confined on the tube surface, on
trajectories that are not modified by curvature effects. Using an ab-initio
approach based on Density Functional Theory we show that this assumption fails
at the nano-scale inducing important corrections to the physics of the
Aharonov-Bohm effect. Curvature effects and electronic density spilled out of
the nanotube surface are shown to break the periodicity of the gap
oscillations. We predict the key phenomenological features of this anomalous
Aharonov-Bohm effect in semi-conductive and metallic tubes and the existence of
a large metallic phase in the low flux regime of Multi-walled nanotubes, also
suggesting possible experiments to validate our results.
