Abstract
In condensed matter, angular momentum is intimately related to the emergence of topological quantum states, including chiral superconductivity, quantum spin liquids and various chiral quasiparticles. Recently, it has been predicted that microscopic lattice excitations, known as phonons, can carry finite angular momentum, leading to specific physical properties of materials. However, phonon angular momentum has not yet been observed directly. Here we demonstrate that angular momentum conservation results in a macroscopic mechanical torque when applying a time-reversal symmetry-breaking thermal gradient along the chiral axis of single-crystal tellurium. We probe this torque using a cantilever-based device and establish that it changes sign by flipping the chirality or thermal gradient. This behavior disappears in polycrystalline samples that lack a preferred chirality. Our experimental results align well with theoretical calculations. We provide compelling evidence for phonon angular momentum, which might enable quantum states with potential applications in microelectronics.
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Data availability
The data that support the findings of this study are available from the corresponding authors upon request. Source data are provided with this paper.
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Acknowledgements
We thank A. Christianson, C. Hua, R. Hermann, A. May, M. McGuire, B. Sales, R. Zhang and T. Zhang for stimulating discussions. This research (torque measurement, crystal growth and part of the numerical calculations) was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. N.P. and Y.Z. (numerical calculations) were supported by the Max Planck Partner laboratory for quantum materials of the Max Planck Institute Chemical Physics of Solids.
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H.M. conceived of the project. H.Z. designed and performed the experiments with help from F.Y., T.Z.W., J.-Q.Y. and H.M. N.P. and Y.Z. performed the theoretical calculations. H.Z., P.R., L.L., C.F., Y.Z., J.-Q.Y. and H.M. analysed and interpreted the experimental data. H.Z., Y.Z. and H.M. wrote the paper with input from all authors.
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Extended data
Extended Data Fig. 1 Chirality of Te single crystals.
Etching image on fresh surfaces of right-handed (a) and left-handed (b) Te samples for the torque measurements. Red and cyan ‘4-shaped’ polygons represent characteristic features for right- and left-handed Te single crystals, respectively.
Extended Data Fig. 2 Calibration of temperature gradient.
(a) A typical pulse of sample temperature measurement in the dummy-setup. (b) The measured temperature gradient at various temperatures for the dummy-setup. (c) The calculated \(\nabla\)T for the cantilever-setup. The power density, \(J=\left(\frac{{\rm{P}}}{{\rm{A}}}\right)\), where P and A stand for the laser power and sample cross-area, respectively.
Extended Data Fig. 3 Torque response of right-handed Te single crystal.
Position dependent scan of thermally activated torque response for a right-handed Te single crystal.
Extended Data Fig. 4 Laser power (P) dependence of τ.
Cantilevers 1 and 2 show opposite torque. The magnitude of ∆τ approximately follows a linear dependence of laser power and consistent with the theoretical estimation of Eq. (4), δJph∝∆T.
Supplementary information
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Source Data Fig. 2
Statistical source data.
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Source Data Extended Data Fig./Table 2
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Source Data Extended Data Fig./Table 4
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Zhang, H., Peshcherenko, N., Yang, F. et al. Measurement of phonon angular momentum. Nat. Phys. 21, 1387–1391 (2025). https://doi.org/10.1038/s41567-025-02952-3
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DOI: https://doi.org/10.1038/s41567-025-02952-3
