Theory of Coulomb Blockade in Carbon Nanotubes

我们提出了一种具有Tomonaga-Luttinger液岛两端连接FL电极（TLL C-SET）的电容耦合单电子晶体管结构中库仑阻塞的自一致微观理论。TLL C-SET岛的候选者是碳纳米管和量子线。在该理论中，费米液体电极的电荷效应和Tomonaga-Luttinger性质被基于C-SET理论的考虑零模式的开边界玻色子化技术以一致的方式处理。得到了TLL C-SET中隧穿电流在任意环境阻抗下的最低阶隧穿哈密顿量的解析表达式，合理地描述了Tomonaga-Luttinger液体中库仑阻塞引起的电流-电压特性。我们表明，在超小但有限的Tomonaga-Luttinger液体中，幂律的相互作用依赖指数除了与接触（体或边）性质相关外，还与系统尺寸相关。研究了碳纳米管和碳纳米管家族的电子特性。讨论了核磁共振弛豫率、自旋激发和局部电荷密度的弗里德尔振荡。未来，在将TLL理论具体应用于碳纳米管的基础上，进一步扩展本研究提出的理论，以了解实验发现的电流-电压特性的细节。

We proposed a self-consistent microscopic theory of the Coulomb blockade in the capacitively coupled single-electron transistor structure with Tomonaga-Luttinger liquid island connected with FL electrodes at both ends (TLL C-SET). Candidates for the island of TLL C-SET are carbon nanotubes and quantum wires. In this theory, the charging effect and the Tomonaga-Luttinger nature are treated in a consistent manner by the open boundary bosonization technique with consideration of zero modes based on the theory of C-SET for Fermi liquid electrodes. Analytical expression of the tunneling current in TLL C-SET is obtained up to the lowest order with respect to the tunneling Hamiltonian for arbitrary environmental impedance and it reasonably describes current-voltage characteristics caused by Coulomb blockade in Tomonaga-Luttinger liquid. We showed that, in the ultrasmall but finite Tomonaga-Luttinger liquid, interaction-dependent exponent of the power law has system size dependence in addition to contact- (bulk- or edge-) nature dependence.Electronic properties of carbon nanotube and carbon nanotube families are also studied. NMR relaxation rate, spin excitation and Friedel oscillation of local charge density are discussed. In future, based on the specific TLL theory to carbon nanotubes, the theory proposed in this research should be extended in order to understand the details of the current-voltage characteristics experimentally found.