Electronic Properties of Nanotubes

Doctoral thesis, 2004

This thesis deals with various aspects of the electronic properties of carbon nanotubes and of generic nanotubes in magnetic fields. Carbon nanotubes are highly symmetric objects on the nanometer scale which show an interesting interplay of their geometry with electronic properties. The geometry is entirely defined by two integer numbers that specify a chiral vector. This vector in turn determines the main electronic properties of a given tube, which can be theoretically understood in terms of a simple tight-binding model. After reviewing these basic facts we move on to use these straight-forward theoretical tools in order to establish a number of fundamental and sometimes surprising properties of nanotubes, such as the effects of the small intrinsic curvature, rehybridization, structural deformations and magnetic fields. Interestingly, rehybridization of the π-orbitals always takes place. As a result, the π orbitals are not oriented along the normal to the surface but rather tilt, with an angle which is a function of the radius and the chiral angle. Consequently, we predict a radial charge redistribution and a small distortion of STM images. The gaps of semi-conducting and primary metallic tubes are determined by an interplay of deformation, curvature, and field effects that can lead to interesting experimental signatures, which have in fact been tested recently. The possibility of universal behavior of tubes with similar radius, but different chiralities under doping is proposed. Following carbon nanotubes, we discuss carbon nanotori and show that in an ensemble of perfect nanotori, the ratio of primary-metallic to semiconducting tori should be almost reversed compared to the one-third to two-thirds in nanotubes. Finally we consider the effects of perpendicular and parallel magnetic fields in nanotubes. Already for generic tubes, i.e. a cylindrical two-dimensional electron gas in a perpendicular magnetic field interesting spin- and charge effects can be observed, such as chiral spin currents. At a certain filling, the current is confined to flow only at the sides of the tube, like the edge states in the Hall bar, giving rise to an integer quantum Hall effect. We then show that some of these effects can also be seen in a curved, not necessary cylindrical, two-dimensional electron gas. The possible experimental realizations of these predictions are discussed.