paper

Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation

arXiv:2412.01280 · doi:10.1103/zvt2-yb2p

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 LiGaS $_{2}$ , LiInSe $_{2}$ , Ca $_{2}$ Al $_{2}$ Si(HO $_{4}$ ) $_{2}$ , Ca $_{7}$ GeN $_{6}$ , Al(HO) $_{3}$ , NaNd(GaS $_{2}$ ) $_{4}$ , Ga $_{5}$ (PS) $_{3}$ and RbTh $_{3}$ F $_{13}$ . The visible phonon drumhead surface states corresponding to the nodal loops in the Hopf-link structure are further demonstrated using Ga $_{5}$ (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.

See Ancillary files for Supporting_Information.pdf