石墨烯纳米带的量子自旋霍尔效应：边缘几何形状的影响
Quantum Spin Hall Effect in Graphene Nanoribbons: Effect of Edge Geometry
摘要：
由Kane和Mele提出的石墨烯体系的拓扑绝缘体的实现方法最近取得了巨大的进展。他们提出，石墨烯的奇数$Z_2$指数表明石墨烯纳米带的自旋过滤边缘态，这导致量子自旋霍尔效应（QSHE）。在这里，我们调查的锯齿形和扶手椅纳米带的边缘几何形状特别小心的自旋-轨道相互作用的作用。对于原始的锯齿形纳米带，我们已经表明，位于E=0附近的其中一个$σ$边缘带通过扭曲$π$边缘带来提高区边界处的自旋过滤手征边缘态的能量，因此QSHE不会发生。当载流子密度增加到某一临界值以上时，形成自旋过滤边缘态，导致QSHE。我们认为边缘的氢钝化可以恢复QSHE的原始特征。对于扶手椅纳米粒子，QSHE被证明是稳定的。我们还导出了实空间有效哈密顿量，表明在带边缘附近的在位能和有效自旋轨道耦合强度都得到了增强。我们已经表明，这样得到的约束势的陡升是造成$π$边带弯曲的原因。
英文摘要：
There has been tremendous recent progress in realizing topological insulator initiated by the proposal of Kane and Mele for the graphene system. They have suggested that the odd $Z_2$ index for the graphene manifests the spin filtered edge states for the graphene nanoribbons, which lead to the quantum spin Hall effect(QSHE). Here we investigate the role of the spin-orbit interaction both for the zigzag and armchair nanoribbons with special care in the edge geometry. For the pristine zigzag nanoribbons, we have shown that one of the $σ$ edge bands located near E=0 lifts up the energy of the spin filtered chiral edge states at the zone boundary by warping the $π$-edge bands, and hence the QSHE does not occur. Upon increasing the carrier density above a certain critical value, the spin filtered edge states are formed leading to the QSHE. We suggest that the hydrogen passivation on the edge can recover the original feature of the QSHE. For the armchair nanoribbon, the QSHE is shown to be stable. We have also derived the real space effective hamiltonian, which demonstrates that the on-site energy and the effective spin orbit coupling strength are strongly enhanced near the ribbon edges. We have shown that the steep rise of the confinement potential thus obtained is responsible for the warping of the $π$-edge bands.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
