Hexagonal Zr₃X (X = Al, Ga, In) Metals: High Dynamic Stability, Nodal Loop, and Perfect Nodal Surface States

In recent years, topological semimetals/metals, including nodal point, nodal line, and nodal surface semimetals/metals, have been studied extensively because of their potential applications in spintronics and quantum computers. In this study, we predict a family of materials, Zr₃X (X = Al, Ga, In), hosting the nodal loop and nodal surface states in the absence of spin-orbit coupling. Remarkably, the energy variation of the nodal loop and nodal surface states in Zr₃X are very small, and these topological signatures lie very close to the Fermi level. When the effect of spin-orbit coupling is considered, the nodal loop and nodal surface states exhibit small energy gaps (<25 and 35 meV, respectively) that are suitable observables that reflect the spin-orbit coupling response of these topological signatures and can be detected in experiments. Moreover, these compounds are dynamically stable, and they consequently form potential material platforms to study nodal loop and nodal surface semimetals.