Dirac phonons in two-dimensional materials

Phonons are an ideal platform for realizing stable spinless two-dimensional (2D) Dirac points because they have a bosonic nature and hard-to-break time-reversal symmetry. It should be noted that the twofold degenerate nodal points in the phonon dispersions of almost all reported 2D materials are misclassified as ``Dirac points'' owing to a historical issue. The correct name for these twofold degenerate nodal points should be ``Weyl'' because 2D phononic systems are essentially spinless and because each twofold degenerate point is described by a Weyl model in two dimensions. To date, reports of fourfold degenerate Dirac point phonons in 2D materials are lacking. In this paper, we searched through all 80 layer groups (LGs) and discovered that Dirac phonons can be realized in 7 of the 80 LGs. Moreover, the Dirac points in the phonon dispersions of 2D materials can be divided into essential and accidental degenerate points, which appear at high-symmetry points and on high-symmetry lines, respectively. Guided by symmetry analysis, we identified the presence of Dirac phonons in several 2D material candidates with six LGs. This work offers a method for identifying Dirac phonons in 2D and proposes 2D material candidates for realizing Dirac phonons.