First-principles calculations for structural, elastic, electronic, and phonon properties of topological WC-type TMO (TM = Ti, Zr and Hf; O) family

Abstract

Through first-principles calculation, we have explored the first three (TiO, ZrO, and HfO) WC-type topological semimetal compounds in transition metal oxides and studied their structural, thermodynamic, elastic, electronic, and dynamical properties systematically. Among these three compounds, only TiO has been experimentally reported as a WC-type, and the other two, ZrO and HfO, are supposed to be WC-type materials. Our density functional theory derived results confirmed that these three compounds are structurally, thermodynamically, mechanically, and dynamically stable, which means they can be easily synthesized. The R. Hill approximation is used to calculate the actual bulk and shear modulus of the single crystal phase with the help of resultant elastic constants and the bulk and shear modulus of the W. Voigt and A. Reuss schemes. Among these compounds, TiO has a high bulk, shear modulus, and low passion ratio, which are directly linked to the high hardness of this compound. Furthermore, TiO is quite an unusual candidate due to the co-existence of 3-fold fundamental particles (3-fold fermions and 3-fold bosons) in the electronic band structure and phonon dispersion along the same Γ-A direction in the Brillouin zone, respectively, providing a perfect platform to explore the probable multi-functional quantum-mechanical properties of these two fundamental particles in a single crystal at the atomistic level. The spin-orbital coupling effect is ignored in TiO due to the light atomic masses of Ti and O elements, and their electronic and topological properties have been more studied.