Jakovljević Dušan Z, Grujić Marko M, Tadić Milan Ž, Peeters François M
School of Electrical Engineering, University of Belgrade, PO Box 3554, 11120 Belgrade, Serbia.
J Phys Condens Matter. 2018 Jan 24;30(3):035301. doi: 10.1088/1361-648X/aa9e67.
Due to nonzero intrinsic spin-orbit interaction in buckled honeycomb crystal structures, silicene and germanene exhibit interesting topological properties, and are therefore candidates for the realization of the quantum spin Hall effect. We employ the Kane-Mele model to investigate the electron states in hexagonal silicene and germanene nanorings having either zigzag or armchair edges in the presence of a perpendicular magnetic field. We present results for the energy spectra as function of magnetic field, the electron density of the spin-up and spin-down states in the ring plane, and the calculation of the probability current density. The quantum spin Hall phase is found at the edges between the nontrivial topological phase in silicene and germanene and vacuum. We demonstrate that the helical edge states in zigzag silicene and germanene nanorings can be qualitatively well understood by means of classical magnetic moments. However, this is not the case for comparable-sized armchair nanorings, where the eigenfunctions spread throughout the ring. Finally, we note that the energy spectra of silicene and germanene nanorings are similar and that the differences between the two are mainly related to the difference in magnitude of the spin-orbit coupling.
由于在翘曲蜂窝状晶体结构中存在非零的本征自旋 - 轨道相互作用，硅烯和锗烯展现出有趣的拓扑性质，因此是实现量子自旋霍尔效应的候选材料。我们采用凯恩 - 梅勒模型来研究在垂直磁场存在下具有锯齿形或扶手椅形边缘的六角形硅烯和锗烯纳米环中的电子态。我们给出了作为磁场函数的能谱、环平面中自旋向上和自旋向下态的电子密度以及概率电流密度的计算结果。在硅烯和锗烯的非平凡拓扑相和真空之间的边缘处发现了量子自旋霍尔相。我们证明，通过经典磁矩可以定性地很好理解锯齿形硅烯和锗烯纳米环中的螺旋边缘态。然而，对于尺寸相当的扶手椅形纳米环情况并非如此，其本征函数遍布整个环。最后，我们注意到硅烯和锗烯纳米环的能谱相似，两者之间的差异主要与自旋 - 轨道耦合大小的差异有关。
