RESUMEN

Nontrivial topological properties in materials have been found in either the electronic or the phononic bands, but they have seldom been shown in both for a compound. With the aid of first-principle calculations, our paper attempts to find topological features in the electron and phonon band structures of ZGeSb (Z = Hf, Zr, Ti) class of compounds. The electron band structure exhibits two nodal rings in each of these compounds. Furthermore, drumhead surface states (DSS) have also been shown. The phonon band structure depicts one nodal ring in each of these compounds. DSS is also seen in the phonon surface states. Layering possibility has also been explored in HfGeSb, which admits a nodal ring each in its electronic and phononic band structure. Finally, these compounds (bulk and mono-layer) possess Dirac points robust to spin-orbit coupling effects, with at least one such Dirac point with its linear dispersion extending to the Fermi energy. Therefore, these compounds fall under the topological nodal line metals class, which is rarely seen in materials. These compounds' theoretical nontrivial topological nature in their electronic and phononic band structure provides a profound grasp of electronic and phononic nodal-line physics and is a good candidate for experimental verification. The existence of Dirac points close to the Fermi level could also motivate one to look for extreme magnetoresistance in these compounds. Moreover, given their largely metallic nature, these compounds become an excellent arena for novel device applications.