Valley coupling in finite-length metallic single-wall carbon nanotubes
Valley coupling in finite-length metallic single-wall carbon nanotubes
复制标题
有限长度金属单壁碳纳米管中的谷耦合
DOI：
10.1103/physrevb.91.235442
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发表时间：
2015
影响因子：
3.7
通讯作者：
R. Saito
中科院分区：
文献类型：
--
作者：
W. Izumida;R. Okuyama;R. Saito
有限长度金属单壁碳纳米管的离散能级简并取决于纳米管的类型、边界条件、长度和自旋轨道相互作用。金属-1纳米管中布里渊带的两个非等效谷相对于管轴具有不同的轨道角动量，由于自旋-轨道相互作用，表现出近四倍的简并度和小的简并度升力，反映了本征函数中两个谷的解耦。在两个谷具有相同轨道角动量的金属-2纳米管中，在正交边缘或帽端边界出现游标尺度的光谱，反映了强谷耦合和狄拉克态的不对称速度。在具有最小边界的较短纳米管中，宇称分裂的四重简并提升克服了自旋轨道相互作用。在纳米管表面曲率引起的能隙中出现了缓慢衰减的倏逝模式。有效的一维晶格模型揭示了边界对特征函数谷耦合的作用。
Degeneracy of discrete energy levels of finite-length, metallic single-wall carbon nanotubes depends on the type of nanotubes, boundary condition, length of nanotubes, and spin-orbit interaction. Metal-1 nanotubes, in which two nonequivalent valleys in the Brillouin zone have different orbital angular momenta with respect to the tube axis, exhibit nearly fourfold degeneracy and small lift of the degeneracy by the spin-orbit interaction reflecting the decoupling of two valleys in the eigenfunctions. In metal-2 nanotubes, in which the two valleys have the same orbital angular momentum, vernier-scale-like spectra appear for boundaries of orthogonal-shaped edge or cap termination reflecting the strong valley coupling and the asymmetric velocities of the Dirac states. Lift of the fourfold degeneracy by parity splitting overcomes the spin-orbit interaction in shorter nanotubes with a so-called minimal boundary. Slowly decaying evanescent modes appear in the energy gap induced by the curvature of nanotube surface. Effective one-dimensional lattice model reveals the role of boundary on the valley coupling in the eigenfunctions.