Ideal topological Weyl complex phonons in two dimensions.

The advent of topological phonons has been attracting tremendous attention. However, studies in two-dimensional (2D) systems are limited. Here, we reveal a 2D novel combination of Weyl phonons - a Weyl complex composed of two linear Weyl nodes and one quadratic Weyl node. This Weyl complex consists of crossing points of two specific branches. We show that the coexistence of threefold symmetry - rotation symmetry, inversion symmetry, and time-reversal symmetry - could lead to the presence of the Weyl complex. Based on the symmetry requirement, we further construct the tight-binding model and effective