Electronic structure and nontrivial topological surface states in ZrRuP and ScPd₃ compounds

In this paper, we investigate the topological properties of ZrRuP and ScPd$_{3}$ using the first-principles calculations. We calculate the electronic structure, surface states, and Z$_{2}$ topological invariant. The band structure of ZrRuP without the spin-orbit coupling (SOC) exhibits a nodal line located at $\Gamma$-K-M high symmetry line in the Brillouin zone(BZ). The nodal line is protected by the mirror symmetry corresponding to the plane $k_{z}=0$. The geometry of Fermi surface is a connected torus centered at K point with open orbits at the boundary of BZ, when the Fermi level is shifted up 0.25 eV. The inclusion of SOC leads to the gap opening in the band structure which corresponds adiabatically to transition from nodal line semimetal to topological insulator. The corresponding surface states were obtained from thin film calculations, and the result shows surface states emerging along the gap region. We also identify the ScPd$_{3}$ compound as a Dirac nodal line semimetal. This structure has nontrivial surface states and the corresponding Z$_{2}$ topological invariant is (1;000). Both the ScPd$_{3}$ and ZrRuP have the Fermi surfaces of the bands which make nodal lines with open orbits.