Cubic Hafnium Nitride: A Novel Topological Semimetal Hosting a 0-Dimensional (0-D) Nodal Point and a 1-D Topological Nodal Ring

Very recently, topological semimetals with nontrivial band crossing and associated topological surface states have received widespread attention. Various types of topological semimetals, including nodal point semimetals, nodal line semimetals, and nodal surface semimetals, have been predicted from first principles. In absence of spin-orbit coupling (SOC) effect, we propose that cubic-type hafnium nitride (HfN) with a [Formula: see text] space group is a novel topological semimetal hosting a rare 0-D triple nodal point and a 1-D topological nodal ring. More importantly, the interesting 0-D and 1-D topological states all occur near the Fermi level, and these topological states are not disturbed by other extraneous bands. When the SOC effect is taken into consideration, 0-D triple nodal point was gapped and a new 0-D topological element, namely, Dirac point appears along Γ-R path. Finally, the dynamical and mechanical stabilities of this semimetal and its associated mechanical properties are discussed in order to provide a reference for future investigations. Our work promises that HfN can serve as a superior topological semimetal with high stability, excellent mechanical properties, and rich topological states.