Double-Weyl Phonons in Transition-Metal Monosilicides

We employed ab initio calculations to identify a class of crystalline materials of MSi (M=Fe, Co, Mn, Re, Ru) having double-Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed "spin-1 Weyl point" at the Brillouin zone center and "charge-2 Dirac point" at the zone corner. The corresponding gapless surface phonon dispersions are two helicoidal sheets whose isofrequency contours form a single noncontractible loop in the surface Brillouin zone. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions.