  An anomalous magnetic flux periodicity of the ground state is predicted in
two-dimensional cylindrical surface composed of square and honeycomb lattice.
The ground state and persistent currents exhibit an approximate fractional
period of the flux quantum for a specific Fermi energy. The period depends on
the aspect ratio of the cylinder and on the lattice structure around the axis.
We discuss possibility of this nontrivial periodicity in a heavily doped
armchair carbon nanotube.
