Electronic States in a Finite Carbon Nanotube: A One-Dimensional Quantum Box

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Abstract
The theoretical scanning-tunneling-spectroscopy image catalog of quantized molecular orbitals of finite armchair carbon nanotubes deposited on a gold (111) surface is presented. Just four different three-dimensional standing-wave (SW) patterns are obtained for electrons close to the Fermi level. The experimental observations of a SW modulation of 0.74 nm and peak pairing in line scans are understood in sight of our results. We show that SW patterns can be explained in terms of the simple Hückel model, but the associated energies, relevant to spectroscopic and transport measurements, are very sensitive to different effects beyond that model including the relaxed geometry, the electronic self-consistency in the finite tubes, and the interaction with the substrate.