Symmetry-Enforced Weyl Phonons

In spinful electronic systems, time-reversal symmetry makes that all Kramers pairs at the time-reversal-invariant momenta are Weyl points (WPs) in chiral crystals. Here, we find that such symmetry-enforced WPs can also emerge in bosonic systems ($e.g.$ phonons and photons) due to nonsymmorphic symmetries. We demonstrate that for some nonsymmorphic chiral space groups, several high-symmetry $k$-points can host $only$ WPs in the phononic systems, dubbed symmetry-enforced Weyl phonons (SEWPs). The SEWPs, enumerated in Table I, are pinned at the boundary of the three-dimensional (3D) Brillouin zone (BZ) and protected by nonsymmorphic crystal symmetries. By performing first-principles calculations and symmetry analysis, we propose that as an example of SEWPs, the two-fold degeneracies at P are monopole WPs in K$_2$Sn$_2$O$_3$ with space group 199. The two WPs of the same chirality at two nonequivalent P points are related by time-reversal symmetry. In particular, at $\sim 17.5$ THz, a spin-1 Weyl phonon is also found at H, since two Weyl phonons at P carrying a non-zero net Chern number cannot exist alone in the 3D BZ. The significant separation between P and H points makes the surface arcs long and clearly visible. Our findings not only present an effective way to search for WPs in bosonic systems, but also offer some promising candidates for studying monopole Weyl and spin-1 Weyl phonons in realistic materials.