Symmetry-enforced nodal chain phonons

Topological phonons in crystalline materials have been attracting great interest. Most cases studied so far are direct generalizations of the topological states from electronic systems. Here, we reveal a class of topological phonons - the symmetry-enforced nodalchain phonons, which manifest the characteristic of phononic systems. We show that in five space groups with D_2d little co-group at a non-time-reversal-invariant-momentum point, the phononic nodal chain is guaranteed to exist owing to the vector basis symmetry of phonons, which is a character distinct from electronic and other systems. In other words, this symmetry enforcement feature of the proposed nodal chain is limited to phononic systems. Interestingly, the chains in these five space groups exhibit two different patterns: for tetragonal systems, they are one-dimensional along the fourfold axis; for cubic systems, they form a threedimensional network structure. Based on first-principles calculations, we identify K₂O as a realistic material hosting the proposed nodal-chain phonons. We show that the effect of LO-TO splitting helps to expose the nodal-chain phonons in a large frequency window. In addition, the nodal chains may lead to drumhead surface phonon modes on multiple surfaces of a sample.