Angular momentum and topology in semiconducting single-wall carbon nanotubes
Angular momentum and topology in semiconducting single-wall carbon nanotubes
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DOI：
10.1103/physrevb.93.195442
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发表时间：
2016-05-31
影响因子：
3.7
通讯作者：
Saito, R.
中科院分区：
文献类型：
--
作者：
Izumida, W.;Okuyama, R.;Saito, R.
利用谷态轨道角动量将半导体单壁碳纳米管分为两类，这对研究有限长半导体单壁碳纳米管的低能电子性质具有重要意义。通过分析切割线，由整数d给出分类，该整数d是指定纳米管的手性的两个整数n和m的最大公约数。对于d大于或等于4的情况，来自两个谷的两个最低子带相对于纳米管轴具有不同的角动量。反映了两个谷的退耦，在有限长的纳米管的离散能级表现出四倍简并和四倍简并的自旋轨道相互作用的小提升。对于d小于或等于2的情况，其中来自两个谷的两个最低的子带具有相同的角动量，离散能级表现出反映两个谷的耦合的四倍简并的提升。特别地，当手征性接近扶手椅手征性时，两个谷强耦合。通过提取具有相关角动量的态，得到了一个有效的一维晶格模型，揭示了本征态中的谷耦合。体-边对应，这是边缘状态的数量和相应的体系统中计算的缠绕数之间的关系，通过使用的幅角原理，解析地示出，这使我们能够估计的边缘状态的数量从体属性。边缘态的数目不仅与手性有关，还与边界的形状有关。
Semiconducting single-wall carbon nanotubes are classified into two types by means of the orbital angular momentum of the valley state, which is useful to study their low-energy electronic properties in finite length. The classification is given by an integer d, which is the greatest common divisor of two integers n and m specifying the chirality of nanotubes, by analyzing cutting lines. For the case that d is greater than or equal to four, the two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit fourfold degeneracy and small lift of fourfold degeneracy by the spin-orbit interaction. For the case that d is less than or equal to two, in which the two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit a lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, which is a relationship between the number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, and this enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.