Abstract
Topological states in quantum materials are defined by bulk wave functions that possess nontrivial topological invariants. While edge modes are widely presented as signatures of nontrivial 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 nontrivial phonon dynamical structure factor, S(Q,ω), 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.
| Original language | English |
|---|---|
| Article number | 184301 |
| Journal | Physical Review B |
| Volume | 103 |
| Issue number | 18 |
| DOIs | |
| State | Published - May 4 2021 |
Funding
This research at Oak Ridge National Laboratory (ORNL) was sponsored by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (IXS data analysis) and by the Laboratory Directed Research and Development Program of ORNL, managed by UT-Battelle, LLC, for the U.S. Department of Energy (IXS experiment). Part of IXS data interpretation work at Brookhaven National Laboratory was supported by the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences, and Engineering Division under Contract No. DE- SC0012704 and by the U.S. DOE, Office of Basic Energy Sciences, Early Career Award Program under Award No. 1047478. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility, operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Extraordinary facility operations were supported, in part, by the DOE Office of Science through the National Virtual Biotechnology Laboratory, a consortium of DOE national laboratories focused on the response to COVID-19, with funding provided by the Coronavirus CARES Act. T.T.Z. and S.M. acknowledge the supports from Tokodai Institute for Element Strategy (TIES) funded by MEXT Elements Strategy Initiative to Form Core Research Center. T.T.Z. also acknowledge the support by Japan Society for the Promotion of Science (JSPS), KAKENHI Grant No. 21K13865. S.M. also acknowledges support by JSPS KAKENHI Grant No. JP18H03678. H.C.L. acknowledges the supports from the National Key R&D Program of China (Grants No. 2016YFA0300504 and No. 2018YFE0202600), the National Natural Science Foundation of China (Grants No. 11774423 and No. 11822412), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grants No. 18XNLG14 and No. 19XNLG17).