No abstract

The search for new topological states has been shifted from electronic fermionic states to phononic bosonic ones, and topological elements with conventional linear band crossing have also been extended into the high order dispersion field. In this Letter, based on theoretical calculations and effective model analysis, we predicted the quadratic phonon states in the hexagonal compound Li2NaN. Particularly, two quadratic nodal lines are found, which are distributed along the same straight Γ–A path, protected by the [Formula: see text] point group symmetry. The detailed band surface distribution and effective Hamiltonian construction are elucidated, demonstrating the quadratic order dispersion. These two quadratic nodal lines were further categorized into type-I and type-III, and their surface spectral properties were calculated, in which clear drumhead surface states are observed for both quadratic nodal lines, and they stretched throughout the entire Brillouin zone. Furthermore, the surface states were well separated from the bulk band projection, which is extremely beneficial for experimental detection. Notably, phononic quadratic nodal line states have been rarely studied and, more importantly, a type-III line has even not been reported thus far. Therefore, our work can pave the way for related studies for both quadratic nodal lines and type-III states, and the presented material can serve as an ideal candidate to promote further experimental investigation.

In this study, we have presented a systematic theoretical study about the electronic, magnetic and structural properties of the full-Heusler compound Fe2CuSi based on first principles calculations. The L21-type structure with ferromagnetic configuration is determined to be the ground state. The calculated electronic band structures show metallic behavior for both spin direction and the obtained total magnetic moment of [Formula: see text]B is mostly contributed from the two Fe atoms, which exhibit strong spin splitting effect as revealed from the partial densities of states. Moreover, both mechanical and dynamic stabilities have been accessed and confirmed for Fe2CuSi under its equilibrium ground-state structure. Besides, multiple mechanical parameters have been calculated and they can provide valuable reference for its practical applications. Lastly, we also evaluate the tetragonal phase by introducing tetragonal strain of [Formula: see text] ratio and results show that the cubic phase maintains the lowest total energy throughout the whole studied strain range, even with [Formula: see text] cell volume variations.

The equiatomic quaternary Heusler compound TiZnMnSi exhibits strong tendency to tetragonal phase transformation.