Abstract
In systems of charged chiral fermions out of equilibrium, an electric current parallel to a magnetic field can generate a dynamic instability that amplifies electromagnetic waves. Whether this mechanism also operates in chiral solid-state systems has remained uncertain. Here we observe signatures of a dynamic magneto-chiral instability in elemental tellurium, a structurally chiral crystal, using time-domain terahertz emission spectroscopy. Under transient photoexcitation in a moderate magnetic field, we observe terahertz radiation with coherent modes that grow in amplitude over time. We present a theoretical model that describes this behaviour based on a dynamic instability of electromagnetic waves interacting with infrared-active oscillators of acceptor states in tellurium, giving rise to an amplifying polariton. These results demonstrate that magneto-chiral instabilities can emerge in solid-state systems and establish a mechanism for terahertz-wave amplification in chiral materials.
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References
Fukushima, K., Kharzeev, D. E. & Warringa, H. J. Chiral magnetic effect. Phys. Rev. D. 78, 074033 (2008).
Akamatsu, Y. & Yamamoto, N. Chiral plasma instabilities. Phys. Rev. Lett. 111, 052002 (2013).
Akamatsu, Y. & Yamamoto, N. Chiral Langevin theory for non-Abelian plasmas. Phys. Rev. D. 90, 125031 (2014).
Shovkovy, I. A. in Peter Suranyi 87th Birthday Festschrift A Life in Quantum Field Theory (eds Argyres, P. et al.) 291–316 (World Scientific, 2023).
Boyarsky, A., Fröhlich, J. & Ruchayskiy, O. Self-consistent evolution of magnetic fields and chiral asymmetry in the early universe. Phys. Rev. Lett. 108, 031301 (2012).
Yamamoto, N. Chiral transport of neutrinos in supernovae: neutrino-induced fluid helicity and helical plasma instability. Phys. Rev. D 93, 065017 (2016).
Most, E. R. Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants. Phys. Rev. D 108, 123012 (2023).
Hirono, Y., Kharzeev, D. E. & Yin, Y. Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly. Phys. Rev. D 92, 125031 (2015).
Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016).
Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).
Zhang, N. et al. Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium. Proc. Natl Acad. Sci. USA 117, 11337–11343 (2020).
Nishida, Y. Chiral light amplifier with pumped Weyl semimetals. Phys. Rev. Lett. 130, 096903 (2023).
Kusunose, H., Kishine, J. -i & Yamamoto, H. M. Emergence of chirality from electron spins, physical fields, and material-field composites. Appl. Phys. Lett. 124, 260501 (2024).
Inda, A., Oiwa, R., Hayami, S., Yamamoto, H. M. & Kusunose, H. Quantification of chirality based on electric toroidal monopole. J. Chem. Phys. 160, 184117 (2024).
Chen, Y., Wu, S. & Burkov, A. A. Axion response in Weyl semimetals. Phys. Rev. B 88, 125105 (2013).
Ma, J. & Pesin, D. A. Chiral magnetic effect and natural optical activity in metals with or without weyl points. Phys. Rev. B 92, 235205 (2015).
Zhong, S., Moore, J. E. & Souza, I. Gyrotropic magnetic effect and the magnetic moment on the Fermi surface. Phys. Rev. Lett. 116, 077201 (2016).
Calavalle, F. et al. Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires. Nat. Mater. 21, 526–532 (2022).
Furukawa, T., Shimokawa, Y., Kobayashi, K. & Itou, T. Observation of current-induced bulk magnetization in elemental tellurium. Nat. Commun. 8, 954 (2017).
Caldwell, R. S. & Fan, H. Y. Optical properties of tellurium and selenium. Phys. Rev. 114, 664–675 (1959).
Dekorsy, T., Auer, H., Bakker, H. J., Roskos, H. G. & Kurz, H. THz electromagnetic emission by coherent infrared-active phonons. Phys. Rev. B 53, 4005–4014 (1996).
Tani, M. et al. Terahertz radiation from coherent phonons excited in semiconductors. J. Appl. Phys. 83, 2473–2477 (1998).
Johnston, M. B., Whittaker, D. M., Corchia, A., Davies, A. G. & Linfield, E. H. Simulation of terahertz generation at semiconductor surfaces. Phys. Rev. B 65, 165301 (2002).
Shan, J., Weiss, C., Wallenstein, R., Beigang, R. & Heinz, T. Origin of magnetic field enhancement in the generation of terahertz radiation from semiconductor surfaces. Opt. Lett. 26, 849–851 (2001).
Barkhuijsen, H., de Beer, R., Bovée, W. & van Ormondt, D. Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure. J. Magn. Reson. 61, 465–481 (1985).
Led, J. J. & Gesmar, H. Application of the linear prediction method to NMR spectroscopy. Chem. Rev. 91, 1413–1426 (1991).
Huang, Y. et al. Nonthermal bonding origin of a novel photoexcited lattice instability in SnSe. Phys. Rev. Lett. 131, 156902 (2023).
Torrie, B. Raman spectrum of tellurium. Solid State Commun. 8, 1899–1901 (1970).
Tanuma, S. The effect of thermally produced lattice defects on the electrical properties of tellurium. Sci. Rep. Res. Inst. Tohoku Univ. Ser. A 6, 159–171 (1954).
Couder, Y., Hulin, M. & Thomé, H. Cyclotron resonance in tellurium. Phys. Rev. B 7, 4373–4385 (1973).
Betbeder-Matibet, O. & Hulin, M. Semi-empirical model for the valence band structure of tellurium. Phys. Status Solidi B 36, 573–586 (1969).
Tani, T. & Tanaka, S. Pressure effect on the impurity state and impurity conduction in tellurium. In The Physics of Selenium and Tellurium: Proc. International Conference on the Physics of Selenium and Tellurium (eds Gerlach, E. & Grosse, P.) 142–152 (Springer, 1979).
Natori, K., Ando, T., Tsukada, M., Nakao, K. & Uemura, Y. The acceptor states in tellurium. J. Phys. Soc. Jpn. 34, 1263–1270 (1973).
Hardy, D., Rigaux, C., Vieren, J. P. & Hau, N. H. Impurities and intervalence band magneto-optical transitions in tellurium. Phys. Status Solidi B 47, 643–653 (1971).
Shinno, H., Yoshizaki, R., Tanaka, S., Doi, T. & Kamimura, H. Conduction band structure of tellurium. J. Phys. Soc. Jpn 35, 525–533 (1973).
Jnawali, G. et al. Ultrafast photoinduced band splitting and carrier dynamics in chiral tellurium nanosheets. Nat. Commun. 11, 3991 (2020).
Dressel, M., Grüner, G. Electrodynamics of Solids: Optical Properties of Electrons in Matter (Cambridge Univ. Press, 2002).
Bottom, V. E. The Hall effect and electrical resistivity of tellurium. Science 115, 570–571 (1952).
Madelung, O. Semiconductors—Basic Data (Springer Science & Business Media, 2012).
Huang, K. On the interaction between the radiation field and ionic crystals. Proc. R. Soc. Lond. Ser. A 208, 352–365 (1951).
Amitani, T. & Nishida, Y. Dynamical chiral magnetic current and instability in Weyl semimetals. Phys. Rev. B 107, 014302 (2023).
Tutihasi, S., Roberts, G., Keezer, R. & Drews, R. Optical properties of tellurium in the fundamental absorption region. Phys. Rev. 177, 1143 (1969).
Hopkins, M. et al. Temperature dependence of the cyclotron-resonance linewidth in GaAs-Ga1−x AlxAs heterojunctions. Phys. Rev. B 39, 13302 (1989).
He, W.-Y. & Law, K. T. Magnetoelectric effects in gyrotropic superconductors. Phys. Rev. Res. 2, 012073 (2020).
Anastassakis, E. M. in Dynamical Properties of Solids Vol. 4 (eds Horton, G. W. & Maradudin, A. A.) 357 (Elsevier, 1980).
Li, J. J., Chen, J., Reis, D. A., Fahy, S. & Merlin, R. Optical probing of ultrafast electronic decay in Bi and Sb with slow phonons. Phys. Rev. Lett. 110, 047401 (2013).
O’Mahony, S. M. et al. Ultrafast relaxation of symmetry-breaking photo-induced atomic forces. Phys. Rev. Lett. 123, 087401 (2019).
Chang, G. et al. Topological quantum properties of chiral crystals. Nat. Mater. 17, 978–985 (2018).
Ma, J. et al. Unveiling Weyl-related optical responses in semiconducting tellurium by mid-infrared circular photogalvanic effect. Nat. Commun. 13, 5425 (2022).
Chen, J. et al. Topological phase change transistors based on tellurium Weyl semiconductor. Sci. Adv. 8, eabn3837 (2022).
Hirayama, M., Okugawa, R., Ishibashi, S., Murakami, S. & Miyake, T. Weyl node and spin texture in trigonal tellurium and selenium. Phys. Rev. Lett. 114, 206401 (2015).
Suárez-Rodríguez, M. et al. Odd nonlinear conductivity under spatial inversion in chiral tellurium. Phys. Rev. Lett. 132, 046303 (2024).
Nomura, K. C. Optical activity in tellurium. Phys. Rev. Lett. 5, 500–501 (1960).
Rinkel, P., Lopes, P. L. S. & Garate, I. Signatures of the chiral anomaly in phonon dynamics. Phys. Rev. Lett. 119, 107401 (2017).
Li, R., Wang, J., Qi, X.-L. & Zhang, S.-C. Dynamical axion field in topological magnetic insulators. Nat. Phys. 6, 284–288 (2010).
Ooguri, H. & Oshikawa, M. Instability in magnetic materials with a dynamical axion field. Phys. Rev. Lett. 108, 161803 (2012).
Planken, P. C., Nienhuys, H.-K., Bakker, H. J. & Wenckebach, T. Measurement and calculation of the orientation dependence of terahertz pulse detection in ZnTe. JOSA B 18, 313–317 (2001).
Ropagnol, X. et al. Efficient terahertz generation and detection in cadmium telluride using ultrafast ytterbium laser. Appl. Phys. Lett. 117, 181101 (2020).
Huang, Y. & Mahmood, F. Data for observation of a dynamic magneto-chiral instability in photoexcited tellurium. Illinois Data Bank https://doi.org/10.13012/B2IDB-1409842_V3 (2025).
Acknowledgements
We thank E. Speranza, R. Zhang, Y. Liu, T. Hughes and T. P. Devereux for useful discussions. This work was supported by the Quantum Sensing and Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0021238 (project conception, data acquisition and analysis, and manuscript preparation). F.M., Y.L., A.M. and C.L. acknowledge support from NSF Career award no. DMR-2144256 for the development of the experimental set-up. F.M. acknowledges support from the EPiQS programme of the Gordon and Betty Moore Foundation, grant GBMF11069. Y.H. acknowledges support from the IQUIST (Illinois Quantum Information Science and Technology Center) Postdoctoral Fellowship. P.Z was supported by the Center for Emergent Materials, an NSF MRSEC, under award no. DMR-2011876. R.M.F. (theoretical model) was supported by the Air Force Office of Scientific Research under award no. FA9550-21-1-0423. J.N. and N.A. (theoretical model) were partly supported by the US Department of Energy, Office of Science, Office for Nuclear Physics under award no. DE-SC0023861. We acknowledge the use of facilities and instrumentation supported by NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center DMR-2309037. Sample characterization was carried out in part in the Materials Research Laboratory Central Research Facilities, University of Illinois. We thank T. Spila and J. Sebastian Lopez for help with LIBS and X-ray fluorescence spectroscopy measurements.
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Y.H. performed sample characterization, the terahertz emission experiments and the corresponding data analysis. Y.L., A.M., Y.H., C.L. and F.M. designed and built the terahertz emission set-up compatible with a magnetic field. D.P. and J.Y.Y. assisted with the terahertz emission measurements without the echo. N.A., Y.H., P.Z., R.M.F. and J.N. developed the theoretical understanding and modelling of the magneto-chiral instability. E.A.P. performed preliminary synthesis reactions, characterized the sample with four-point conductivity measurements and assisted Y.H. with structural characterization, supervised by D.P.S. D.C. and P.A. provided insights into the acceptor states in tellurium and characterized the sample using X-ray measurements. Y.H., N.A., P.Z., R.M.F., J.N. and F.M. wrote the manuscript with input from all the authors. F.M. initiated and supervised the project.
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Huang, Y., Abboud, N., Lv, Y. et al. Dynamic magneto-chiral instability in photoexcited tellurium. Nat. Phys. 22, 202–208 (2026). https://doi.org/10.1038/s41567-025-03145-8
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DOI: https://doi.org/10.1038/s41567-025-03145-8
