Maslyuk Volodymyr V, Gutierrez Rafael, Cuniberti Gianaurelio
Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden, Germany.
Phys Chem Chem Phys. 2017 Mar 29;19(13):8848-8853. doi: 10.1039/c7cp00059f.
Spin-orbit interaction in carbon nanotubes has been under debate for several years and a variety of theoretical calculations and experimental results have been published. Here, we present an accurate implementation of spin-orbit interactions in a density-functional theory framework including both core and valence orbital contributions, thus using the full potential of the system. We find that the spin-splitting of the frontier bands of armchair nanotubes is of the order of several μeV and does not strongly depend on the diameter of the nanotube. We also provide a systematic analysis of the band splitting in chiral nanotubes as a function of the diameter and the chiral angle. Very good agreement with previous theoretical studies and experimental results is overall found. In particular, our approach can be of great relevance in view of the recently discovered chirality-induced spin selectivity, since it allows us to include not only atomic contributions to the spin-orbit interaction, but more importantly, global contributions to the potential arising from the geometric structure (topology) of the system. Our methodology can thus encode effects such as helical symmetry in a straightforward way.
碳纳米管中的自旋轨道相互作用已经争论了数年，并且已经发表了各种理论计算和实验结果。在这里，我们在密度泛函理论框架内精确实现了自旋轨道相互作用，包括核心和价轨道贡献，从而利用了系统的全部势能。我们发现扶手椅型纳米管前沿能带的自旋分裂约为几个微电子伏特，并且不太强烈地依赖于纳米管的直径。我们还对手性纳米管中的能带分裂作为直径和手性角的函数进行了系统分析。总体上发现与先前的理论研究和实验结果非常吻合。特别是，鉴于最近发现的手性诱导自旋选择性，我们的方法可能具有重要意义，因为它不仅允许我们纳入原子对自旋轨道相互作用的贡献，更重要的是，还能纳入由系统的几何结构（拓扑）产生的势能的全局贡献。因此，我们的方法可以直接编码诸如螺旋对称性等效应。
