Three-dimensional (3D) topological insulators (TIs) have been studied for approximately fifteen years, but those made from group-IV elements, especially Ge and Sn, seem particularly attractive owing to their nontoxicity, sizable intrinsic spin-orbit coupling (SOC) strength and natural compatibility with the current semiconductor industry. However, group-IV elemental TIs have rarely been reported, except for the low temperature phase of α-Sn under strain. Here, based on first-principles calculations, we propose new allotropes of Ge and Sn, named T5-Ge/Sn, as desirable TIs. These new allotropes are also highly anisotropic Dirac semimetals if the SOC is turned off. To the best of our knowledge, T5-Ge/Sn are the first 3D allotropes of Ge/Sn that possess topological states in their equilibrium states at room temperature. Additionally, their isostructures of C and Si are metastable indirect and direct semiconductors. Our work not only reveals two promising TIs, but more profoundly, we justify the advantages of group-IV elements as topological quantum materials (TQMs) for fundamental research and potential practical applications, and thus reveal a new direction in the search for desirable TQMs.

三维 (3D) 拓扑绝缘体 (TI) 已经被研究了大约 15 年，但那些由 IV 族元素，尤其是 Ge 和 Sn 制成的，由于它们的无毒、相当大的内在自旋轨道耦合 (SOC) 似乎特别有吸引力实力和与当前半导体行业的天然兼容性。然而，除了α-Sn在应变下的低温相之外，很少报道IV族元素TI。在这里，基于第一性原理计算，我们提出了 Ge 和 Sn 的新同素异形体，称为 T5-Ge/Sn，作为理想的 TI。如果 SOC 关闭，这些新的同素异形体也是高度各向异性的狄拉克半金属。据我们所知，T5-Ge/Sn 是 Ge/Sn 的第一个 3D 同素异形体，它们在室温下处于平衡态时具有拓扑状态。此外，它们的 C 和 Si 的同构结构是亚稳态的间接和直接半导体。我们的工作不仅揭示了两个有前途的 TI，而且更深刻地证明了 IV 族元素作为拓扑量子材料 (TQM) 在基础研究和潜在实际应用中的优势，从而为寻找理想的 TQM 提供了新方向。