Topological phonon dispersion in multifold Weyl semimetal RhSi

Topology of the quantum mechanical wavefunction has been a core interest of the condensed matter physics and material science community over the past decade. Recent theories predict that it is possible to realize bosonic analogues of such topological phases in materials, namely phononic Weyl systems where there exist topologically protected phonon band crossings in momentum space. Additionally, phononic Weyl materials host surface phonon "arc" states, which are analogous to the Fermi arcs in electronic Weyl semimetals. Based on first principles calculations, transition metal monosilicides are expected to host topological Weyl nodes. Here we use inelastic x-ray scattering (IXS) experiments to measure the bulk phonon dispersion of RhSi, a unique material that is expected to host multifold Weyl nodes in both its electronic and phonon band structure. The IXS experiments are consistent with the phonon calculations based on density functional theory and two distinct types of topological nodes namely spin-1 Weyl and charge-2 Dirac nodes can be identified. Furthermore, using momentum resolved electron energy loss spectroscopy the surface phonon dispersion can be measured, direct experimental evidence for which have hitherto remained elusive.