Chern numbers of topological phonon band crossing determined with inelastic neutron scattering

Topological invariants in the band structure, such as Chern numbers, are crucial for classification of topological matters and dictate occurrence exotic properties, yet their direct spectroscopic determination has been largely limited to electronic bands. Here, we use inelastic neutron scattering conjunction with ab initio calculations identify a variety phonon crossings MnSi CoSi single crystals. We find distinct relation between numbers band-crossing node intensity modulation momentum space around node. Given sufficiently high resolution, our method can be used determine arbitrarily large nodes.