The realization of a Hopf-link structure in the Brillouin zone is rather rare, which hinders comprehensive exploration and understanding of such exotic nodal loop geometry. We tabulated 141 space groups which could host a Hopf-link structure derived from band crossings in high-symmetry lines and then investigated the Phonon Database at Kyoto University, which contains 10 034 materials, to search for phonon realization of the Hopf-link nodal structure based on these space groups. We found that almost all the investigated materials have nodal loops or nodal chains, while only 113 materials can host a Hopf-link structure in phonon spectra, among which 8 representative materials are manually selected to showcase the relatively clean Hopf-link structure, including ${\mathrm{LiGaS}}_2, {\mathrm{LiInSe}}_2, {\mathrm{Ca}}_2{\mathrm{Al}}_2\mathrm{Si}{\left({\mathrm{HO}}_4\right)}_2, {\mathrm{Ca}}_7{\mathrm{GeN}}_6$, Al(${\mathrm{HO})}_3, \mathrm{NaNd}{\left({\mathrm{GaS}}_2\right)}_4, {\mathrm{Ga}}_5{\left(\mathrm{PS}\right)}_3$, and ${\mathrm{RbTh}}_3{\mathrm{F}}_{13}$. The visible phonon drumhead surface states corresponding to the nodal loops in Hopf-link structure are further demonstrated using ${\mathrm{Ga}}_5{\left(\mathrm{PS}\right)}_3$. The listed 113 crystalline materials provide a good platform for experimentalists to further explore the interesting properties related to the Hopf-link structure.

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• First-principles calculations
• Phonons
• Topological materials
• Group theory
• k dot p method