Milan Damnjanović

Phonon dispersion of graphite by inelastic x-ray scattering

We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the

FULL SYMMETRY, OPTICAL ACTIVITY, AND POTENTIALS OF SINGLE-WALL AND MULTIWALL NANOTUBES

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Optical dichroism in nanotubes

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Carbon nanotubes band assignation, topology, Bloch states, and selection rules

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Super-slippery carbon nanotubes

points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the

Line Groups in Physics

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Symmetry of single-wall nanotubes

point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.

Modified group projectors: tight-binding method

The full symmetry groups for all single- and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case, any type of the line and the axial point groups can be obtained, depending on single-wall constituents and their relative position. Several other consequences are discussed: quantum numbers and related selection rules, electronic and phonon bands, and their degeneracy, application to tensor properties.

Symmetry and lattices of single-wall nanotubes

Utilizing the line-group symmetry of single-wall nanotubes, we have assigned their electron-energy bands by the symmetry-based quantum numbers. The selection rules for optical absorption are presented in terms of these quantum numbers. Different interband transitions become allowed as the polarization of incident light is varied, and we predict a substantial optical dichroism. We propose how to observe this effect in experiments on a single nanotube, and how it can be used to control quantum transport in nanotubes to obtain information about the structure.

Interaction between layers of the multi-wall carbon nanotubes

Various properties of the energy band structures ~electronic, phonon, etc.!, including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete set of quantum numbers consists of the angular and linear quasimomenta and parities with respect to the U axis and, for achiral tubes, the mirror planes. The assignation of the electronic bands is performed, and the generalized Bloch symmetry adapted eigen functions are derived. The most important physical tensors are characterized by the quantum numbers. All this enables application of the presented exhaustive selection rules. The results are discussed by some examples, e.g., allowed interband transitions, conductivity, Raman tensor, etc.