Coexistent topological and chiral phonons in chiral RhGe: An ab initio study

The CoSi family of materials (CoSi, CoGe, RhSi, and RhGe) forms a cubic chiral structure and hosts unconventional multifold chiral fermions, such as spin-1 and spin-32 fermions, leading to intriguing phenomena like long Fermi arc surface states and exotic transport properties. Recent interest in the phonon behavior in chiral materials has been growing due to their unique characteristics, including topological phonons, protected surface states, and chiral phonons with nonzero angular momentums. In this study, we explore the topological and chiral phonon behavior in RhGe, using first-principles density functional theory calculations as well as the symmetry and topological analysis. We uncover six spin-1 triply degenerate nodal points at the point and six charge-2 double Weyl points at the R point in the Brillouin zone (BZ). Interestingly, these topological features are identical to that in the electronic band structure of the same material without electron spin-orbit coupling. We expect that this finding not only applies to the CoSi family but also is universal. Secondly, we find that chiral crystal RhGe hosts chiral phonon modes with a phonon angular momentum (PAM) and an associated phonon magnetic moment (PMM), everywhere in the BZ except at high-symmetry points such as, R, X, and M. The PAM and PMM are large along the chiral rotation axis and in the vicinity of the topological nodes. In this study, we also reveal that all the topological phonon modes are chiral. However, the reverse is not always true. Among other things, our finding of the coexistence of topological and chiral phonon modes in chiral RhGe not only deepens our understanding of the phonon behavior in the CoSi family but also opens pathways for developing advanced materials and devices.