Ideal topological phononic nodal chain in K2O materials class

Nodal-chain semimetals are characterized by linked nodal rings in Brillouin zone and they have not been reported in the phonon system of atomic crystals yet. Here, based on first-principles calculations and tight-binding model analysis, we propose nearly ideal nodal chains can be realized in the phonon modes of experimentally synthesized ionic crystal K2O materials class. Different from all previous cases, the connection points of the nodal chain in K2O are located at the high symmetry points W and the positions are limited by the symmetries. The nodal rings that forming the nodal chain are symmetrically equivalent and protected by the mirror symmetries. The nontrivial topological properties of nodal chains are validated by the nontrivial Berry phase and surface modes. A general discussion about all symmorphic space groups reveals that, if no more than two inequivalent mirrors exist, Fm 3 over bar m (No. 225) is a unique space group for the appearance of the nodal chain connected at the high symmetry points. Our studies demonstrate that K2O materials class is a wonderful implementable platform to study the nontrivial topological nodal chains in a phonon system.