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 Yu et al. recently provides a comprehensive list of all potential nodal points for systems with specific space groups [Sci. Bull. 67, 375 (2022)]. 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 fourfold-degenerate (FD) phonons in noncentrosymmetric space groups. Using symmetry arguments and k·p model 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 space group with fourfold degenerate phonons, we propose corresponding materials that must host the fourfold-degenerate points. Our work not only deepens our understanding of the mechanisms underlying the formation of these fourfold-degenerate phonons, but it also proposes practical materials for observing FD phonons in crystalline systems without inversion symmetry.&#xD.