Stable Dirac semimetal in the allotropes of group-IV elements

Three-dimensional topological Dirac semimetals represent a novel state of quantum matter with exoticelectronic properties, in which a pair of Dirac points with a linear dispersion along all momentum directionsexists in the bulk. Herein, by using first-principles calculations, we discover the metastable allotropes of Ge andSn in the staggered layered dumbbell structure, named germancite and stancite, to be Dirac semimetals with apair of Dirac points on their rotation axis. On the surface parallel to the rotation axis, a pair of topologicallynontrivial Fermi arcs are observed and a Lifshitz transition is found by tuning the Fermi level. Furthermore,the quantum thin film of germancite is found to be an intrinsic quantum spin Hall insulator. These discoveriessuggest novel physical properties and future applications of the metastable allotrope of Ge and Sn