Topological insulators in the NaCaBi family with large spin-orbit coupling gaps

Abstract

By means of first-principles calculations and crystal structure searching techniques, we predict that a different NaCaBi family crystallized into the ZrBeSi-type structure (i.e., 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 occurred 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 (T) and inversion symmetry (I), the spinless nodal-line metallic phase protected by [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 6[over ¯] 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 their gaps are smaller than that of NaCaBi. Thus, they provide good platforms to study topological states both in theory and experiments.