We present a comprehensive first-principles investigation of topological phonon band structures in a class of high-symmetry binary compounds of the form $MX$ $(M=\mathrm{Sc}, \mathrm{Y}, \mathrm{La} \text{and} X=\mathrm{Sb}, \mathrm{Bi})$, which crystallize in the face-centered cubic space group $Fm\overline{3}m$. Our phonon dispersion calculations reveal multiple symmetry-protected twofold degeneracies that manifest as nodal rings, nodal chains, and nodal boxes in the Brillouin zone. These topological features are confirmed through the computation of quantized Berry phases. Notably, we identify drumhead-like surface phonon states on the [001] surface, projected along the high-symmetry $\mathrm{\Gamma }$-X-M-$\mathrm{\Gamma }$ path. These flat surface modes are robust against symmetry-preserving perturbations and represent strong topological signatures of the underlying bulk nodal structures. Our findings position these binary $MX$ compounds as promising candidates for realizing phononic topological phases with potential applications in thermal management and surface phononics.

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• Phonons
• Topological materials
• Density functional calculations