Material realization of double-Weyl phonons and phononic double-helicoid surface arcs with P213 space group

Unconventional chiral quasiparticles with twofold, threefold, and fourfold degeneracies and Chern number (C) = ±2 have recently sparked interest because of their topological chirality in momentum space. Herein, based on first-principles calculations and symmetry analysis, we propose 14 synthesized topological phonon systems with space group P213 (No. 198) that host two types of almost-ideal double-Weyl points, which are the fourfold degenerate charge-2 Dirac point and the threefold degenerate spin-1 Weyl point. Based on the projected local density of states on the [100] and [101] surfaces of these selected realistic materials, we discovered two visible winding around the projected double-Weyl points, demonstrating the appearance of phononic double-helical surface arcs. Furthermore, we constructed a k·p model to determine how the two types of double-Weyl point phonons coexist in the system with the P213 space group. We believe that this work provides directions for investigating double-Weyl point phonons and an ideal platform for investigating phononic double-helical surface states in realistic materials.