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Updated: Jul 7, 2026

Fabrication, Densification, and Replica Molding of 3D Carbon Nanotube Microstructures
Published on: July 2, 2012
Reciprocal space constraints create real-space anomalies in doped carbon nanotubes
E R Margine1, Paul E Lammert, Vincent H Crespi
1Department of Physics, The Pennsylvania State University, University Park, PA 16802-6300, USA.
Abstract:
When graphite is doped with electrons, carbon-carbon bonds lengthen and Raman-active phonons soften as antibonding states fill. However, in semiconducting carbon nanotubes, one Raman-active G-band mode increases in frequency at low doping levels. We show how phase constraints on the conduction-band wave function expose a latent bonding character in the conduction band of certain nanotubes. In these tubes, filling the lowest conduction band shortens the axial bonds even as it lengthens the circumferential bonds. The A{1}{LO} phonon, which preferentially stretches the axial bonds, then hardens even as the other phonons soften. Quantum confinement eliminates the angular averaging taken for granted in higher-dimensional systems and develops a new class of states, neither bonding nor antibonding, whose character depends on the angular orientation of the bonds in question.
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