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

Abstract

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-3/2 fermions, leading to intriguing phenomena like long Fermi arc surface states and exotic transport properties. Recent interest on the phonon behavior in chiral materials is growing due to their unique characteristics, including topological phonons, protected surface states and the chiral phonons with non-zero 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. In particular, we uncover six spin-1 triply degenerate nodal points at the $Γ$ 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 without the electron spin-orbit coupling, of the same material. 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 $Γ$, R, X and M. The PAM and PMM are large along the chiral rotation axis and also in the vicinity of the topological nodes. Our study also reveals 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 new pathways for developing advanced materials and devices.