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Numerical calculations of the conductance are performed to study effects of a weak magnetic field or flux on a perfectly conducting channel in metallic carbon nanotubes in the presence of scatterers with potential range larger than the lattice constant. The perfect channel can easily be destroyed even by a very small magnetic field or flux when there are several bands at the energy, while it is much more robust in the energy range of metallic linear bands.
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Tsuneya Ando (2004) studied this question.
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