| The advances in researches for carbon nanotubes (CNTs), such as preparation and purification, physical and chemical properties, technical applications, research fields, methods and achievements are reviewed entirely at first, then the atomic structure, the properties of Brillouin zone of the CNTs and its relations with the graphene are explored and described systematically. Depending on these basis, we place the emphasis on exploration of the electronics of CNTs, including the deep researches of the electronic structure, the properties of the electrical transport, the properties of the magnetic transport and the magnetism of the single-walled carbon nanotubes (SWNTs) or the toroidal carbon nanotubes (TCNTs), etc.In order to research for the unique electronic structure, the analytic expression of the π- electronic energy dispersion (or states) relations for the chiral SWNTs and TCNTs in the two cases of perfection and imperfection are derived by using tight-binding model. It is found that an external magnetic field can induce the change of the energy gaps resulting in the metal-semiconductor continuous transition with magnetic flux Φ in a period Φ = Φ0 (h/e) for the perfect chiral SWNTs and type I and type II TCNTs, this is obvious AB effect. Furthermore, Van Hove singularities exhibit remarkably in electronic density of states (DOS) and the differential electrical conductivity Ga related to the experimental measurements, this is demonstration of one-dimension characteristics of the SWNTs. The deformed metal-SWNTs and metal-TCNTs can be transformed to semiconductor or insulator due to deformations resulting to variation of the atomic structure and the nearest-atom transfer integral having relation with the directions.Based on the Boltzmann transport equation and n - electronic energy dispersion relations for individual SWNTs, the theoretical model caculating the current and conductance of the SWNTs is deduced. The low-temperature conductances of undoping or doping SWNTs are studied numerically, the calculated results show that, for the doping SWNTs, the conductance is quantized, i.e. the conductance exhibits step structure with the bias voltage or electronic transport energy and becomes unobser-vable with the increasing of the temperature T and the tubular diameter dt. For thedoping SWNTs, the current exhibits jump characteristic with varied bias voltage. The properties of current, such as the magnitude, jump period and jump amplitude are not determined entirely by the doping electronic concentration, but depending directly on the tubular diameter and the electronic DOS near Fermi level after SWNTs being doped. The jump structure becomes smooth with the temperature T rising and the tubular diameter increasing. In particular, according to the "wave- particle duality" of the electrons participating transport in the SWNTs, namely, we use the Boltzmann transport equation, in combination with the weak localization (WL) theory to calculate the theoretical value of low- temperature intrinsic resistance of individual SWNTs. The obtained results are in good agreement with measurement in which there exists very low contact resistance.Using the Boltzmann transport equation involving magnetic field , we obtain the theoretical model for calculating the magnetoresistance (MR) of the SWNTs. The calculating results show that, for low-energy electron transport, AB effect is the dominant factor resulting in the weaker AAS effect being covered so that the AB effect can be observed remarkably and MR oscillations are with a period Φ0, whereas for the conducting electrons with higher energy, the AAS effect becomes dominant although its magnitude is still small, but the AB effect is still much weaker and almost vanished, therefore, the MR oscillations have a period Φ/2. If these results extend to individual MWNTs, the contradiction of the currently inconsistent experiment results and theoretical explanation can be solved naturally.The numerical calculations are performed for the magnetism of the chiral TCNTs, the r...
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