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

TL;DR

This study identifies and catalogs materials with Hopf-link phonon spectra, providing a valuable resource for experimental exploration of exotic topological phonon structures and their surface states.

Contribution

It systematically searches for Hopf-link phonon structures in a large database, tabulates 141 suitable space groups, and highlights 113 candidate materials for experimental study.

Findings

113 materials can host Hopf-link phonon structures

8 materials exhibit clear Hopf-link phonon spectra

Surface states associated with Hopf-link structures are demonstrated

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.