On the basis of the Landau quantization, the bound state is discussed, which includes the finite length effect, induced magnetic field, and electric field in a current-carrying nanotube. Using a slab model and evaluating the matching of the wave function in the radial direction, the authors obtained the conditions of a Landau mode in which the momentum in the axial direction is reversed in the outer side and inner side of the nanotube shell. The mode arises over a threshold electric current, influences more long tubes than short tubes, and does not contribute to the net electric current. The authors compared the theoretical results to the experimental data, estimating the minimum voltage condition, the relations between the tube length and the current for the obtained Landau mode, and the tube length and current data in the experiments. It is plausible that the Landau mode plays an important role in the eventual electrical breakdown and the thinning phenomena. The wave function broadly spreading in the outer side in the radial direction activates the air and triggers the destruction of atomic bonds. Another factor influencing the electrical breakdown phenomena was found.
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