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Topological states in quantum materials are defined by non-trivialtopological invariants, such as the Chern number, which are properties of theirbulk wave functions. A remarkable consequence of topological wave functions isthe emergence of edge modes, a phenomenon known as bulk-edge correspondence,that gives rise to quantized or chiral physical properties. While edge modesare widely presented as signatures of non-trivial topology, how bulk wavefunctions can manifest explicitly topological properties remains unresolved.Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined withfirst principles calculations, we report experimental signatures of chiral wavefunctions in the bulk phonon spectrum of BaPtGe, which we show to host apreviously undiscovered twofold degenerate quadruple Weyl node. The chiralityof the degenerate phononic wave function yields a non-trivial phonon dynamicalstructure factor, S(Q,$\omega$), along high-symmetry directions, that is inexcellent agreement with numerical and model calculations. Our resultsestablish IXS as a powerful tool to uncover topological wave functions,providing a key missing ingredient in the study of topological quantum matter.

Observation of a Chiral Wave Function in Twofold Degenerate Quadruple Weyl System BaPtGe