Beyond no-go theorem' Weyl phonons

By using \emph{ab initio} calculations and symmetry analysis, we define a new class of Weyl phonons, i.e., isolated Weyl phonons (IWPs), which are characterized by Chern number $\pm$2 or $\pm$4 in their acoustic phononic spectra and protected by the time inversion symmetry and point group symmetries. More importantly, their particular topological feature make them circumvent from the no-go theorem. Some high-symmetry points, behaving as isolated Weyl points in the space groups (SGs) of the related phononic systems, tend to form IWPs. As enumerated in Table I, the IWPs are located at the center of three-dimensional Brillouin zone (BZ), and protected by the time-reversal symmetry ($\cal T$) and the corresponding point group symmetries. Moreover, a realistic chiral crystal material example of K$_2$Mg$_2$O$_3$ in SG 96, a monopole IWP with Chern number -2 is found at the high-symmetry point $\Gamma$, and in another material example of Nb$_3$Al$_2$N in SG 213, a monopole IWP with Chern number +4 is confirmed at the point $\Gamma$. It is interesting that that IWPs can not form the surface arcs in the surface BZ, which has not been reported in the phononic systems to present. Our theoretical results not only uncover a new class of Weyl phonons (IWPs), but also put forwards an effective way to search the IWPs in spinless systems.