Paired charge-2 Weyl-Dirac phonons in tetragonal crystals

Unconventional Weyl and Dirac phonons with topological charges of $\ifmmode\pm\else\textpm\fi{}2$ have attracted significant attention due to their exceptional properties. By employing a minimal lattice model, we propose that an ideal topological quasiparticle coexistence system can be achieved in chiral space groups 92 and 96. This system specifically incorporates a charge-2 Weyl phonon and a charge-2 Dirac phonon. Notably, the crystal symmetry restricts these two topological quasiparticles to high-symmetry points within the Brillouin zone, resulting in an ultralong surface arc that extends across the entire surface Brillouin zone. Moreover, the topological surface arcs exhibit a unique saddlelike surface feature. Taking ${\mathrm{BaPt}}₂{\mathrm{S}}₃$ as a representative example, we validate our prediction and reveal the interconnected ultralong surface arc and saddlelike topological surface state. Our work establishes a valuable framework for investigating diverse types of double Weyl nodes and presents a promising approach for detecting ultralong surface arcs.