Symmetry-enforced fourfold degenerate phonons in noncentrosymmetric space groups.

Multifold degenerate phonons have received much attention due to their nontrivial monopole topological charge and fascinating boundary states. Although Yuet alrecently provides a comprehensive list of all potential nodal points for systems with specific space groups (SGs) (2022Sci. Bull.67375). However, our understanding of the fundamental mechanisms that give rise to the formation of fourfold-degenerate (FD) phonons is still limited. In this paper, we have directed our research towards investigating the generation mechanism of these FD phonons in noncentrosymmetric SGs. Using symmetry arguments andk⋅pmodel analysis, we have classified them into two categories: the first origins from the commutation/anticommutation relation of the little cogroup operations, and the second associates to the combination of threefold rotation, mirror and time-reversal symmetries. Moreover, the band dispersions of the FD phonons in the first group are required to be linear, whereas the band dispersions of the FD phonons in the second category may be quadratic. On the basis of first-principles calculations, we propose that K2Mg2O3and Na4SnSe4are representative candidates for the two categories, respectively. Furthermore, for each SG with fourfold degenerate phonons, we propose corresponding materials that must host the FD points. Our work not only deepens our understanding of the mechanisms underlying the formation of these FD phonons, but it also proposes practical materials for observing FD phonons in crystalline systems without inversion symmetry.

Slater-Koster parametrization for the phonons of monolayer MoX2(X = S, Se or Te).

With the help of the Slater-Koster parametrization, we construct simplified force constant (FC) models to describe the phonons of several two-dimensional (2D) transition metal dichalcogenides (TMDs) (MoX2, X = S, Se or Te) by only considering the FCs to fourth-nearest-neighbor interactions. By fitting the phonon dispersions derived from first-principles calculations, we find these models can well describe the symmetry characters and semimetal states of MoX2's phonons. Combining the basis of the FC model and the theory of tensor representation, we derive the origin of the irreducible representations at the high symmetry points Γ,KandM. Moreover, by using the compatibility relation between high symmetry points and high symmetry lines, we find the semimetal states of MoX2are protected by vertical and horizontal mirrors. Our work provides an effective tool to further study the phonons of 2D TMDs.