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Vibrational modes of carbon nanotubes: A force-constant model approach

Janina Zimmermann

Diplom (equiv. Master) Thesis, University of Regensburg, March 2006

Until some decades ago, only two types of all-carbon crystalline structure were known: the naturally occurring allotropes diamond and graphite. The breakthrough which revolutionized carbon research came from experiments on clusters formed by laser vaporization on graphite: The discovery first of C60 in 1985 [1] and then of carbon nanotubes by S. Iijima in 1991 [2] marked the beginning of a new era in carbon science. Carbon nanotubes are crystals with the shape of hollow cylinders made of one or more graphite sheets. Soon after their discovery in multiwall form, carbon nanotubes consisting of one single graphitic layer were synthesized [3, 4]. During the past ten years carbon nanotubes (CNTs) have been at the focus of intense experimental and theoretical research. This is due to their potential for applications as well as to the fact that they represent an ideal model system to investigate the physical properties of an ordered, quasi-one-dimensional crystal. From a technological point of view, one of the highlights of nanotube research is the construction of nanotube-based electronic devices, such as single-electron transistors [5] or even logic circuits [6]. Beyond the variety of applications, single-walled CNTs (SWCNTs) are interesting for their fundamental physical properties. With a length of about 1 m and diameters around 1 nm, single-walled CNTs fall into the size range where quantum effects become important and this, combined with their particular symmetries, leads to remarkable electronic, magnetic and vibrational properties. Vibrational properties are the subject of increasing attention for several reasons. Besides the interest in the phonons of a system with such a unique structure [7], detailed knowledge of the vibrational spectrum of CNTs is of central importance for temperature-dependent properties such as charge, spin and heat transport [8], for superconductivity [9], and optical characterization [10]. Recently, particular attention has been paid to the thermal properties of carbon nanotubes since some of their applications may depend significantly on their thermodynamic features. A detailed knowledge of energy dissipation and thermal transport is required for controlling the performance and stability of nanotube-based devices. For this purpose, the role of molecular vibrations might be very relevant. Especially at low temperatures the thermal properties are determined by phonons, rather then by electrons. In this temperature regime carbon nanotubes are characterized by ballistic phonon transport and thermal conductance quantization [11]. [...]

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