Symmetry-enforced ideal lanternlike phonons in the ternary nitride Li6WN4

Topological physics of phonon spectra has been attracting great interest. Using the first-principle calculations and symmetry analysis, we show the realistic ternary nitride ${\mathrm{Li}}_{6}{\mathrm{WN}}_{4}$ features ideal (nearly flat) nodal-surface and nodal-line structures in its phonon spectra. These nodal degeneracies are shaped like lanterns, and their existence is guaranteed by nonsymmorphic symmetry. The corresponding topological phonon surface state covers exactly half the surface Brillouin zone and can thereby be distinguished from those of conventional nodal-line and nodal-surface semimetals. Our study enriches the classification of topological quantum phases, predicts ideal material candidates, and provides a good platform for investigating the interaction between nodal-line and nodal-surface phonons.