Coexistence of topological and chiral phonons in polymorphs of CoGe

The interplay of topology and chirality in non-symmorphic chiral crystals unveils novel quantum phenomena such as chiral anomalies and exotic fermionic excitations with extended Fermi arcs. In this study, we unify two seemingly distinct concepts topological phonons, arising from non-trivial band topology, and chiral phonons, associated with circular polarization and non-zero angular momentum through the lens of Weyl phonons in chiral CoGe phase. Using first-principles calculations, symmetry analysis, and effective modeling, we reveal the entanglement of chiral and topological phonons in the P 2 1 3 phase of CoGe. We show that crystal chirality dictates topological charge, mirror enantiomers host Weyl phonons with opposite charges, distinct surface states, and reversed arc connections. Remarkably, we identify quadruple two-fold degenerate Weyl nodes with a Chern number of ±4 the highest reported for phononic systems. Due to the C 3 rotational symmetry along the Γ-R direction, chiral phonon modes emerge naturally, with circular polarization reversing under mirror operations mirroring the topological charge reversal.We propose helicity-resolved Raman spectroscopy as a powerful tool to detect these chiral phonons, linking circular polarization to Berry curvature and phonon angular momentum.Additionally, we explore a distorted kagome lattice phase (space group P-62m) of CoGe, predicting Dirac nodal lines and triply degenerate phonon points. In this achiral structure, valley-selective chiral phonons emerge at ±K(±H) points, exhibiting opposite circular polarization. Our findings establish CoGe as a versatile platform to explore a wide range of phononic topological quasiparticles, including spin-1/2 Weyl, spin-1 Weyl, charge-2 Dirac, charge-4 Weyl, Dirac nodal lines,type-I and type-III quadratic nodal points, and triply degenerate nodal points.