Carbon Nanotubes in Magnetic Fields

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Carbon nanotubes (CN's) discovered by Iijima are a new class of quantum wire having the structure of two-dimensional (2D) graphite sheet rolled up in a cylindrical form. A CN consists of concentric tubes, each of which has carbon-atom hexagons arranged in a helical fashion about the axis. The distance of adjacent tubes is about 0.34 nm, i.e., roughly the same as the distance of adjacent honeycomb lattice planes of graphite. The dimeter of each tube is usually between about 20 and 300 @90 and the maximum length of a CN exceeds 1mum in general. The purpose of this thesis is to study the effects of magnetic fields on electronic states, optical absorption, lattice instability, and magnetic properties of carbon nanotubes.In this project we have studied effects of magnetic fields on various electronic properties of a single-shell carbon nanotubes. In a magnetic field passing through the tube axis, the band gap changes with the period of the magnetic flux quantum due to the Aharonov-Bohm (AB) effect. The AB effect manifests itself in optical absorption spectra and magnetic properties. In a magnetic field perpendicular to the tube axis, well-defined Landau levels are formed at the Fermi energy originated from that of a 2D graphite. This leads to intriguing properties of CN's including a considerable enhancement of lattice distortion.It was first shown in tight-binding models that a single-shell CN's can be either a metal or semiconductor depending on the diameter and the helical arrangement. A condition for such a characteristic change has been derived based on the band structure of a 2D graphite sheet. In this study, we haveused a k-p method extensively throughout the course of the study and compared the results with those in a tight-binding model whenever necessary. The effective-mass approximation is quite effective in the study of effects of external magnetic and electric fields.