Coexistence of charge-2 Dirac and Weyl phonons in chiral space groups

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Unconventional topological phonons with unusual properties in crystalline solids have attracted increasing attention. By performing symmetry arguments and low-energy effective Hamiltonian, we confirm the coexistence of charge-2 Dirac and Weyl phonons at high-symmetry points and high-symmetry lines by analyzing all possible space groups. We reveal that such a particular system only emerges in chiral space groups in the presence of time-reversal symmetry. Unlike conventional Weyl pairs with opposite chirality that host one surface arc, there are two surface arcs by connecting one charge-2 Dirac point with topological charge = $\ifmmode\pm\else\textpm\fi{}2$ and two Weyl points with topological charge = $\ensuremath{\mp}1$. Due to the constraints of symmetry arguments and projection direction in chiral crystals, the surface arcs are long enough to span over the whole surface Brillouin zone. We take ${\mathrm{Na}}_{2}{\mathrm{Zn}}_{2}{\mathrm{O}}_{3}$ as an example to confirm our predication, and two branches of surface states across the whole surface Brillouin zone are clearly visible. Our work not only presents exotic quasiparticles but also provides an idea for realizing long nontrivial surface arcs.