Diagnosing and observing topological degeneracies in AI class systems

Topological states have been widely studied in Fermionic systems for many years, wherever, they are sporadically explored in Bosonic systems, even both Fermions and Bosons are fundamental particles in condensed matter physics. Actually, Bosons can offer a better platform to get spinless band structures where nodal lines can be realized with only parity-time reversal (PT) symmetry, such as phonons. By combining first-principles calculations and meV-resolution inelastic x-ray scattering, we demonstrate the first realization of PT symmetry protected helical nodal lines of phonons in a real material. The combination of theoretical analysis and experimental measurements demonstrate the PT-protected helical nodal lines for the first time in phononic materials. This nodal line is robust because of the spinless nature of phonons, which will open a new route to explore exotic topological states in crystalline materials.