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 = $\pm 2$ and two Weyl points with topological charge = $\mp 1$. 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.

中文翻译：

---

电荷 2 Dirac 和 Weyl 声子在手性空间群中的共存

在结晶固体中具有不寻常性质的非常规拓扑声子引起了越来越多的关注。通过执行对称论证和低能有效哈密顿量，我们通过分析所有可能的空间群来确认电荷 2 狄拉克和外尔声子在高对称点和高对称线上的共存。我们揭示了这样一个特定的系统仅在存在时间反转对称性的情况下出现在手性空间群中。与拥有一个表面弧的具有相反手性的传统 Weyl 对不同，通过将一个电荷 2 狄拉克点与拓扑电荷连接，有两个表面弧 =$\pm 2$和两个带拓扑电荷的外尔点 =$\mp 1$. 由于手性晶体中对称参数和投影方向的限制，表面弧长足以跨越整个表面布里渊区。我们采取${钠}_2{锌}_2{\mathrm{○}}_3$作为一个例子来证实我们的预测，整个表面布里渊区的两个表面状态分支清晰可见。我们的工作不仅提出了奇异的准粒子，而且还为实现长的非平凡表面弧提供了一种思路。