Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2
Shiang Fang, Linda Ye, Madhav Prasad Ghimire, Min Gu Kang, Junwei Liu, Liang Fu, Manuel Richter, Jeroen van den Brink, Efthimios Kaxiras, Riccardo Comin, Joseph G. Checkelsky
二维kagome晶格在其布里渊区角K和K '处承载狄拉克费米子，类似于蜂窝晶格。在铁磁kagome金属Fe $_3$ Sn $_2$的电子结构的密度泛函理论中，在没有自旋轨道耦合的情况下，我们确定了两个能量分裂的螺旋节线，该节线在K和K'附近沿着$z$缠绕，这是由kagome层的三角堆叠产生的。我们发现，跨越A-A堆叠的跳跃引入了能量的层分裂，而跨越A-B堆叠的跳跃控制了螺旋节线的动量空间振幅。自旋-轨道耦合的效果被发现类似于凯恩-梅勒项，其中的节线可以完全缺口准二维大质量狄拉克费米子，或保持在离散的外尔点取决于铁磁矩取向的间隙。除了在数值上建立Fe $_3$ Sn $_2$作为模型狄拉克kagome金属，我们的研究结果提供了深入了解材料设计的拓扑相从晶格的角度来看，其中范例低维晶格模型往往发现实现在晶体材料的三维堆叠。
英文摘要：
The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K', analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K' resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing Fe$_3$Sn$_2$ as a model Dirac kagome metal, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.
Realization of Kane-Mele Model in $\pmb X\bf{N_4}$-Embedded Graphene ($\pmb X$=Pt, Ir, Rh, Os)
嵌入有过渡金属氮化物的单层石墨烯（即，$X$ N $_4$），其中过渡金属原子与四个氮原子一起作为单元嵌入石墨烯中以形成稳定的平面单原子厚度结构。我们利用第一性原理计算和紧束缚模型对这些$X$ N $_4$嵌入石墨烯的结构、电子和拓扑性质进行了系统的研究。我们发现$X$ N $_4$嵌入的石墨烯（$X$ =Pt，Ir，Rh，Os）可以打开容纳\emph{two-dimensional} $\mathbb{Z}_2$拓扑绝缘体的拓扑非平凡带隙。我们进一步表明，带隙附近的低能带可以被一个修改的凯恩-梅勒模型哈密顿量完美地捕获。我们的工作不仅提供了实现\emph{two-dimensional} $\mathbb{Z}_2$拓扑绝缘体的非常罕见的具体二维材料，而且使石墨烯体系在承载Kane-Mele型$\mathbb{Z}_2$拓扑绝缘体方面成为现实。
