Influence of delocalized states on electron scattering by carbon nanotubes under various configurations

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Abstract
In the family of electron projection microscopes, the Fresnel projection microscope (FPM) allows observation in direct space of small organic fibers such as carbon nanotubes, with electron energies about 200 eV. With carbon nanotube material the optical Fresnel theory fails to explain all the features observed experimentally. We have performed simulations of FPM images of carbon nanotubes by combining quantum-mechanical electron diffusion theory with an ab initio method to include the properties of the molecular object. Simulations done with a (5,5) nanotube do reproduce the experimental occurrence of a very bright and contrasted geometrical projection of thin fibers, the so-called “sucking-in” effect. Furthermore, they allow to link this phenomenon with the large spreading of the effective potential occurring with nanotubes. Patterns in the simulated images of multiwall carbon nanotubes and ropes of nanotubes are reported. They are mainly governed by interferences occurring between the scattered waves coming from the different nanotubes. Ropes lead to large fringes unlike multiwall nanotubes, which lead to constructive interferences between the scattered waves. This constructive behavior is pointed out by means of a chiral inner nanotube, which leads to specific longitudinal fringes and an asymmetric pattern of the images as it is also reported for single-wall chiral nanotubes.