From Topological Nodal-Line Semimetal to Insulator in ABW-Ge₄: A New Member of the Germanium Allotrope

Topological semimetals have attracted much attentionbecause oftheir excellent properties, such as ultra-high speed, low energy consumptionquantum transport, and negative reluctance. Searching materials withtopological semimetallic properties has become a new research fieldfor Group-IV materials. Herein, using first-principles calculationsand tight-binding modeling, we proposed a topological nodal-line semimetalABW-Ge-4 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 electronicband structure, there exists a stable Dirac linear band crossing nearthe Fermi energy level, which forms a closed ring in the k ( x ) = 0 plane of the Brillouin zone (BZ).Our symmetry analysis reveals that the nodal ring is protected by M ( x ) mirror symmetry. Furthermore,by examining the slope index in all possible k paths through the considered Dirac point, we find thatthe band dispersion near the Dirac point is greatly anisotropic. Insome direction, the Fermi velocity is even larger than that of graphene,being promising for the future ultra-high speed device. When spin-orbitcoupling is included, the nodal line is gapped and the system becomesa topological insulator with topological invariants Z (2) = 1. Our findings not only identify a new Ge allotropebut also establish a promising topological material in Group-IV materials,which may have the desirable compatibility with the traditional semiconductorindustry.