  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.
