Charge-four Weyl phonons

Abstract

By using ab initio calculations and symmetry analysis, we define a class of Weyl phonons: charge-four Weyl phonons (CFWPs) characterized by Chern number $\ifmmode\pm\else\textpm\fi{}4$ in their acoustic phonon spectra due to chiral point-group symmetries. Some high-symmetry points in the chiral space groups (SGs) of phononic systems behaving as quadratic Weyl points tend to form CFWPs. As enumerated in this paper, the CFWPs are located at the boundaries or the center of the three-dimensional Brillouin zone and are protected by the time-reversal symmetry $\mathcal{T}$ and the corresponding point-group symmetries. Moreover, in a realistic chiral crystal example of BiIrSe in SG 198, a monopole CFWP is confirmed at point $\mathrm{\ensuremath{\Gamma}}$ with quadratic twofold degeneracies, and in another example of ${\mathrm{Li}}_{3}{\mathrm{CuS}}_{2}$ in SG 214, the CFWPs are found at the high-symmetry points $\mathrm{\ensuremath{\Gamma}}$ and $H$. Our theoretical results not only uncover a class of Weyl phonons but also put forward an effective way to search for CFWPs in spinless systems.