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

Li, Haoxiang; Zhang, Tiantian; Said, A.; Fu, Y.; Fabbris, G.; Mazzone, D. G.; Zhang, J.; Lapano, J.; Lee, H. N.; Lei, H. C.; Dean, M. P. M.; Murakami, S.; Miao, H.

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