This paper gives a short review of some of our theoretical understanding of the structural and electronic properties of single-walled carbon nanotubes and of various structures formed from these nanotubes. Because of their nanometer dimensions, the nanotube structures can have novel properties and yield unusual scientific phenomena. In addition to the multi-walled carbon nanotubes, single-walled nanotubes, nanotube ropes, nanotube junctions, and non-carbon nanotubes have been synthesized.

These quasi-one-dimensional objects have highly unusual electronic properties. For the perfect tubes, theoretical studies have shown that the electronic properties of the carbon nanotubes are intimately connected to their structure. They can be metallic or semiconducting, depending sensitively on tube diameter and chirality. Experimental studies using transport, scanning tunneling, and other techniques have basically confirmed the theoretical predictions. The dielectric responses of the carbon nanotubes are found to be highly anisotropic in general. The heat capacity of single-wall nanotubes is predicted to have a characteristic linear T dependence at low temperature.

On-tube metal-semiconductor, semiconductor-semiconductor, and metalmetal junctions may be formed by introducing topological structural defects, and these junctions have been shown to behave like nanoscale device elements. For example, different half-tubes may be joined with 5-member ring/7-member ring pair defects to form a metal-semiconductor Schottky barrier. The calculated electronic structure of these junctions is very similar to that of standard metal-semiconductor interfaces, and in this sense, they are molecular level devices composed of the single element, carbon. Recent experimental measurements have confirmed the existence of such Schottky barrier behavior in nanotube ropes and across kinked nanotube junctions. Similarly, 5-7 defect pairs in different carbon and non-carbon nanotubes can produce semiconductor-semiconductor and metal-metal junctions. The existence of metal-metal nanotube junctions in which the conductance is suppressed for symmetry reasons has also been predicted. Thus, the carbon nanotube junctions may be used as nanoscale electronic elements.

The influence of impurities and local structural defects on the conductance of carbon nanotubes has also been examined. It is found that local defects in general form well defined quasi-bound states even in metallic nanotubes. These defect states give rise to peaks in the LDOS and reduce the conductance at the energy of the defect levels by a quantum unit of conductance via resonant backscattering. The theoretical studies show that, owing to the unique electronic structure of the graphene sheet, the transport properties of (n, n) metallic tubes appear to be very robust against defects and long-range perturbations near EF. Doped semiconducting tubes are much more susceptible to long-range disorder. These results explain the experimental findings of the long coherence length in metallic tubes and the large difference in mean free path between the metallic and doped semiconducting tubes. For nanotube ropes, intertube interactions are shown to alter the electronic structure of (n, n) metallic tubes because of broken symmetry effects, leading to a pseudogap in the density of states and to semimetallic behavior. Crossed-tube junctions have also been fabricated experimentally and studied theoretically. These systems show significant intertube conductance for metal-metal junctions and exhibit Schottky behavior for metal-semiconductor junctions when the tubes are subjected to contact force from the substrate.

The carbon nanotubes are hence a fascinating new class of materials with many unique and desirable properties. The rich interplay between the geometric and electronic structure of the nanotubes has given rise to many interesting, new physical phenomena. At the practical level, these systems have the potential for many possible applications.

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