title: Reciprocal space constraints create real-space anomalies in doped carbon nanotubes.
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.
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, PA 16802-6300, USA.
authors.forename: E R
authors.initials: ER
authors.lastname: Margine
authors.forename: Paul E
authors.initials: PE
authors.lastname: Lammert
authors.forename: Vincent H
authors.initials: VH
authors.lastname: Crespi