Carbon nanotubes provide a unique system to study one-dimensional quantization phenomena. Scanning tunneling microscopy is used to observe the electronic wave functions that correspond to quantized energy levels in short metallic carbon nanotubes. Discrete electron waves are apparent from periodic oscillations in the differential conductance as a function of the position along the tube axis, with a period that differs from that of the atomic lattice. Wave functions can be observed for several electron states at adjacent discrete energies. The measured wavelengths are in good agreement with the calculated Fermi wavelength for armchair nanotubes.
@article{arxiv.cond-mat/9811317,
title = {Imaging Electron Wave Functions of Quantized Energy Levels in Carbon Nanotubes},
author = {Liesbeth C. Venema and Jeroen W. G. Wildoer and Jorg W. Janssen and Sander J. Tans and Hinne L. J. Temminck Tuinstra and Leo P. Kouwenhoven and Cees Dekker},
journal= {arXiv preprint arXiv:cond-mat/9811317},
year = {2009}
}