Phononic higher-order nodal point in two dimensions

Fermionic quasiparticles in solids have attracted tremendous attention in the last decades. The conceptual framework of quasiparticles has recently been extended to bosonic systems, especially the phononic one. In this work we focus on a peculiar phononic topological category that features higher-order nodal points in twodimensional (2D) systems. By searching through the total 80 layer groups, we find that the rotation symmetry (except the twofold one) combined with the time-reversal symmetry could support the presence of higher-order nodal points. We further find that the highest order of momentum in the 2D system is the second order, dubbed as quadratic nodal point (QNP). We show that the 2D QNP can be characterized by an integer topological invariant, demonstrated by the presence of edge states. Remarkably, this work reveals the mechanism for the band structure deforming, such as the tilting of the QNP cone and the warping of constant frequency surfaces. The work paves the way to study the higher-order nodal point in phononic systems, and several candidate materials are also provided.