Multiply charged topological phonons in $K_2{\mathrm{Pb}}_2{O}_3$

Topological phonons have attracted tremendous attention in recent years, particularly when topological phonons have nonzero topological numbers and exhibit many peculiar physical phenomena. However, studies on the coexistence of different phonons with nonzero topological charge are quite limited. Here, we reveal a realist material $K_2{\mathrm{Pb}}_2{O}_3$, which can realize the coexistence of three types of phonons, namely charge-1 Weyl point (WP), charge-2 triple point (TP), and charge-4 WP. We perform symmetry analysis for these points, presenting symmetry conditions to realize these topological phonons, and constructing an effective model to describe them. Meanwhile, we calculate the phonon spectrum, topological surface states, and the constant frequency slice for $K_2{\mathrm{Pb}}_2{O}_3$, and we perform the Wilson loop method to calculate the Chern number for WPs and TPs in the material. The results indicate that the material $K_2{\mathrm{Pb}}_2{O}_3$ has charge-1 WPs, charge-2 TPs, and charge-4 WPs at high-symmetry points in the range of 13–19 THz. In particular, the phonon spectrum within this range solely contains the bands responsible for forming these topological band-crossing points. The Fermi arcs emanating from the projections of a charge-1 WP, a charge-2 TP, and a charge-4 WP are connected with each other, forming a long Fermi arc extended in the whole Brillouin zone, which greatly facilitates observation in experiment by neutron scatterings or high-resolution electron energy loss spectroscopy. Our work provides a platform for studying charge-1 WP, charge-2 TP, and charge-4 WP in a phononic system.