Carbon Nanotubes in Magnetic Fields

碳纳米管（CN's）是由Iijima发现的一种新型量子线，其结构为二维（2D）石墨片卷成圆柱形。CN由同心管组成，每个同心管都有围绕轴以螺旋方式排列的碳原子六边形。相邻管的距离约为0.34 nm，即，与石墨的相邻蜂窝状晶格平面的距离大致相同。每个管的直径通常在约20和300@90之间，CN的最大长度通常超过1 μ m。本论文的目的是研究磁场对碳纳米管的电子态、光吸收、晶格不稳定性和磁性质的影响，在本项目中我们研究了磁场对单壳层碳纳米管的各种电子性质的影响。在穿过管轴的磁场中，由于Aharonov-Bohm（AB）效应，带隙随磁通量子的周期而变化。AB效应表现在光学吸收光谱和磁性上。在垂直于管轴的磁场中，在源于二维石墨的费米能级处形成了定义明确的朗道能级。紧束缚模型首次表明，单壳层CN可以是金属，也可以是半导体，这取决于其直径和螺旋排列。基于二维石墨片的能带结构导出了这种特性变化的条件。在本研究中，我们在整个研究过程中广泛使用了k-p方法，并在必要时将结果与紧束缚模型中的结果进行了比较。有效质量近似是研究外磁场和电场效应的有效方法。

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.