By using first-principles calculations and symmetry analysis, we uncover that the rubidium-catena-telluridoaurate-family materials in space group (SG) 51 can exhibit ideal nodal-surface phonons separately in the three-dimensional Brillouin zone, characterized by nearly flat phonon bands in their phonon spectra. The nodal surfaces are protected both by the screw rotation symmetry and the time reversal symmetry. Moreover, our theoretical calculations demonstrate that the nodal surfaces are composed by twofold degenerate nodal points, which can form a straight singularity nodal line in the (001) surface, and that the (001) surface states display Dirac-type crossings and surface flat-band phononic states, confirming the topologically nontrivial nature of nodal-surface phonons. Our findings not only support that another class of nodal phononic states, i.e., one-node surface phonons, can exist in realistic materials in 230 SGs, but also put forward an effective way to search for nodal-surface phonons.

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• Acoustic phonons
• Magnetism
• Symmetry protected topological states
• Density functional calculations