Two-dimensional Dirac phonons without/with inversion symmetry

In a recent study, two-dimensional Dirac phonons that are protected by nonsymmorphic symmetries in spinless systems were systematically investigated. However, the focus of this study was on the classification of Dirac phonons. To address the gap in the research on the topological features of 2D Dirac phonons based on their effective models, we classified the 2D Dirac phonons into two classes: without or with inversion symmetry, thereby clarifying the minimal symmetry requirements for enforcing 2D Dirac points. Based on symmetry analysis, we discovered that screw symmetries, together with time-reversal symmetry, play an essential role in the existence of Dirac points. To validate this result, we constructed the k & BULL;p model to describe the Dirac phonons and discussed their topological features accordingly. We found that a 2D Dirac point could be considered as a composition of two 2D Weyl points with opposite chirality. Furthermore, we provided two concrete materials to demonstrate our findings. Overall, our work provides a more detailed study of 2D Dirac points in spinless systems and clarifies their topological features.