  Three-dimensional topological insulators 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 alpha-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 state 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.
