Spectroscopic Analysis of Quantum Size Effects in Single Wall Carbon Nanotubes

Single wall Carbon nanatubes are new forms of carbon derived from large and elongated fullerenes or from rolled up graphene sheets. Typical diameters of the tubes are 1.5 nm while their length can be up to 104 nm. Because of their unique geometry and of the particular bonding of the carbon atoms, the nanotubes have a large application potential in the field of nanomechanics and nanoelectronics. Depending on the geometry of the rolling up process, different chiralities of the tubes are obtained. The tubes represent perfect one-dimensional periodic systems with the size of the unit cell given by their chirality and diameter. Because of the small size of the tube diameter the wave functions of the electrons correspond to discrete wave vectors in the xy plane of the graphene sheet and the electronic densities of states exhibit divergencies for each of these waves. From the preparation always distributions of tubes with different chirality and different diameter are obtained. In the proposed research project structural and electronic properties of the tubes will be investigated by Raman and IR spectroscopy. This is possible, since the vibrational modes are also discrete and their energy depends on the chirality of the tubes. In the case of Raman experiments, photoselective resonance scattering plays an important role. Using different laser energies, tubes with different chirality will be excited in resonance. This means, spectroscopic experiments can be performed on different tubes even for the case, that the tubes are only available with a distribution of chiralities. From the observed Raman cross sections information on the electronic structures of the tubes can be drawn. The goal of the research work is, amongst others, to find conditions for the preparation of nanotubes with a predefined chirality and a predefined diameter. The research work will be performed in cooperation with a research group at the University of North Carolina in USA and at the Eötvös University in Budapest.

Single wall Carbon nanotubes are new forms of carbon derived from large and elongated fullerenes or from rolled up graphene sheets. Typical diameters of the tubes are 1.35 nm while their length can be up to 104 nm. Because of their unique geometry and of the particular bonding of the carbon atoms, the nanotubes have a large application potential in the field of nanomechanics and nanoelectronics. Depending on the geometry of the rolling up process, different tubes are obtained. The tubes represent perfect one- dimensional periodic systems with the size of the unit cell given by their structure and diameter. Because of the small size of the tube diameter the wave functions of the electrons correspond to discrete wave vectors in the xy plane of the graphene sheet and the electronic densities of states exhibit divergencies for each of these waves. From the preparation always distributions of tubes with different structure and different diameter are obtained. In the research project performed first a procedure was elaborated which allows to determine the mean tube diameter and the width of the diameter distribution for single wall carbon nanotube material. The procedure uses the mean position of the Raman response from the radial breathing mode of the tubes. It is redundant for excitation with different laser lines and thus allows even to determine the root mean square error if several different lasers are used for the analysis. The procedure was tested for samples of carbon nanotubes with three different diameters ranging from 1 nm to 1.6 nm. From a careful inspection of the Raman response for the radial breathing mode an oscillatory behavior for the mean line position and for the deviation of this mean position was observed for the excitation with a large number of different laser lines. These oscillations could be traced back to size quantization of the electronic states with wave functions propagating perpendicular to the tube axis. For a Raman line which was induced by defect states a similar but less expressed oscillation was observed. From a calculation using a tight binding band structure an fits to ab initio calculated phonon dispersion relations a quantitative agreement with the experiments could be obtained. This calculation is based on a new resonance scattering mechanism which involves a triple resonant excitation including the van Hove singularities in the densities of states. The research work was performed in cooperation with a research group at the University of the Tokyo Metropolitan University in Japan and at the Eötvös University in Budapest.