Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
Abstract
The realization of Hopf-link structure in the Brillouin zone is rather rare hindering the comprehensive exploration and understanding of such exotic nodal loop geometry. Here we first tabulate 141 space groups hosting Hopf-link structure and then investigate Phonon Database at Kyoto University consisting of 10034 materials to search for phonon realization of the Hopf-link nodal structure. It is found that almost all the investigated materials own nodal loops or nodal chains while only 113 materials can host Hopf-link structure in phonon spectra, among which 8 representative materials are manually selected to showcase relatively clean Hopf-link structure including LiGaS2, LiInSe2, Ca2Al2Si(HO4)2, Ca7GeN6, Al(HO)3, NaNd(GaS2)4, Ga5(PS)3 and RbTh3F13. The visible phonon drumhead surface states corresponding to the nodal loops in the Hopf-link structure are further demonstrated using Ga5(PS)3 as an example.The listed 113 crystalline materials provide a good platform for experimentalists to further explore the interesting properties related to Hopf-link structure.
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