Physical property of a single quantum object is governed by its precise atomic arrangement. The direct correlation of localized physical properties with the atomic structures has been therefore strongly desired but still limited in the theoretical studies. Here, we have successfully examined the localized electronic properties of individual carbon nanotubes by means of high-resolution electron energy-loss spectroscopy combined with high-resolution transmission electron microscopy. Well-separated sharp peaks at the carbon K(1s) absorption edge and in the valence-loss spectra are obtained from a single freestanding carbon nanotube with the local chiral index and unambiguously identified as the transitions between the van Hove singularities. The spectra features clearly vary upon the different areas even in the individual carbon nanotube. Variations in interband transitions, plasmonic behaviors, and unoccupied electronic structures are clearly attributed to the local irregular atomic arrangement such as topological defect and/or elastic bond stretching.
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