From Topological Nodal-Line Semimetal to Insulator in ABW-Ge: A New Member of the Germanium Allotrope.

Topological semimetals have attracted much attention because of their excellent properties, such as ultra-high speed, low energy consumption quantum transport, and negative reluctance. Searching materials with topological semimetallic properties has become a new research field for Group-IV materials. Herein, using first-principles calculations and tight-binding modeling, we proposed a topological nodal-line semimetal ABW-Ge when spin-orbit coupling (SOC) is ignored, which is composed of pure germanium atoms in a zeolite framework ABW. It holds excellent dynamic and thermal stability. In its electronic band structure, there exists a stable Dirac linear band crossing near the Fermi energy level, which forms a closed ring in the = 0 plane of the Brillouin zone (BZ). Our symmetry analysis reveals that the nodal ring is protected by mirror symmetry. Furthermore, by examining the slope index in all possible paths through the considered Dirac point, we find that the band dispersion near the Dirac point is greatly anisotropic. In some direction, the Fermi velocity is even larger than that of graphene, being promising for the future ultra-high speed device. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with topological invariants = 1. Our findings not only identify a new Ge allotrope but also establish a promising topological material in Group-IV materials, which may have the desirable compatibility with the traditional semiconductor industry.