Charge-two Weyl phonons with type-III dispersion

In recent years, charge-two Weyl point phonons (WPPs) have attracted increasing attention. Charge-two WPPs not only provide a new platform for realizing phonon-based unconventional Weyl points (WPs) but also help in realizing specific phonon-based transport behaviors. Herein, based on the first-principles calculations and symmetry analysis, we propose a realistic material with the $P{3}_{1}21$ space group, ${\mathrm{BaZnO}}_{2}$, which has a charge-two WPP and two charge-one WPPs at high-symmetry points. These three unpaired WPPs form a unique triangular Weyl complex. Unlike previously reported material candidates with type-I or type-II charge-two WPPs, the proposed ${\mathrm{BaZnO}}_{2}$ has a type-III charge-two WPP, which has a constant frequency surface that contains two electronlike or holelike states connected at the charge-two WP. ${\mathrm{BaZnO}}_{2}$ can support double-helicoid phonon surface states that cover the entire (001) surface Brillouin zone. The clean type-III WPP, unique triangular Weyl complex, and clear and long surface states in ${\mathrm{BaZnO}}_{2}$ suggest that it is an excellent platform for further research into the physics and applications of type-III charge-two WPPs. Furthermore, we pointed out that charge-two WPPs with type-III band dispersion may appear at high-symmetry points in space groups 75--80, 89--98, 143--146, 149--155, 168--173, 177--182, 196, 207--210. Besides trigonal ${\mathrm{BaZnO}}_{2}$, some material candidates, including tetragonal ${\mathrm{MgTiO}}_{4}$, trigonal ${\mathrm{Li}}_{2}{\mathrm{GeF}}_{6}$, hexagonal ${\mathrm{CaSO}}_{4}$, and cubic ${\mathrm{Li}}_{10}{\mathrm{B}}_{14}{\mathrm{Cl}}_{2}{\mathrm{O}}_{25}$, are also shown to be the hosts of type-III charge-two WPPs.