具有大SOC间隙的NaCaBi族拓扑绝缘体
Topological insulators in the NaCaBi family with large SOC gaps
摘要：
通过第一性原理计算和晶体结构搜索技术，我们预测了一个新的具有ZrBeSi型结构的NaCaBi族（\ie $P6_{3}/mmc$）是强拓扑绝缘体。以$P6_{3}/mmc$ NaCaBi为例，计算的能带结构表明在$Γ$点处两个相反宇称带之间存在带反转.与众所周知的Bi $_2$ Se $_3$族相比，NaCaBi族中的能带反转甚至在没有自旋轨道耦合（SOC）的情况下已经发生，从而在$k_z=0$平面中产生围绕$Γ$的节环（受$M_z$对称性保护）。在时间反演对称性$(\cal T)$和反演对称性$(\cal I)$的作用下，由$[{\cal TI}]^2=1$保护的无自旋金属线相是有自旋拓扑绝缘相的弱SOC极限.在包括SOC时，节点环是有间隙的，将系统驱动到STI。NaCaBi的非平凡拓扑结构除了具有反演对称性外，还可以用$\bar{6}$对称性来表示.更令人惊讶的是，在NaCaBi中SOC诱导的带隙为约0.34eV，这大于室温的能量标度。该家族中的其他四种化合物（KBaBi，KSrBi，RbBaBi和RbSrBi）在常压下在热力学和晶格动力学上都是稳定的，尽管它们的间隙小于NaCaBi。因此，它们为从理论和实验上研究拓扑态提供了良好的平台。
英文摘要：
By means of first-principles calculations and crystal structure searching techniques, we predict that a new NaCaBi family crystallized into the ZrBeSi-type structure (\ie $P6_{3}/mmc$) are strong topological insulators (STIs). Taking $P6_{3}/mmc$ NaCaBi as an example, the calculated band structure indicates that there is a band inversion between two opposite-parity bands at the $Γ$ point. In contrast to the well-known Bi$_2$Se$_3$ family, the band inversion in the NaCaBi family has already occured even without spin-orbit coupling (SOC), giving rise to a nodal ring surrounding $Γ$ in the $k_z=0$ plane (protected by $M_z$ symmetry). With time reversal symmetry $(\cal T)$ and inversion symmetry $(\cal I)$, the spinless nodal-line metallic phase protected by $[{\cal TI}]^2=1$ is the weak-SOC limit of the spinful topological insulating phase. Upon including SOC, the nodal ring is gapped, driving the system into a STI. Besides inversion symmetry, the nontrivial topology of NaCaBi can also be indicated by $\bar{6}$ symmetry. More surprisingly, the SOC-induced band gap in NaCaBi is about 0.34 eV, which is larger than the energy scale of room temperature. Four other compounds (KBaBi, KSrBi, RbBaBi and RbSrBi) in the family are stable at ambient pressure, both in thermodynamics and lattice dynamics, even though the gaps of them are smaller than that of NaCaBi. Thus, they provide good platforms to study topological states both in theory and experiments.
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