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Acoustic Landau quantization and quantum-Hall-like edge states


Many intriguing phenomena occur for electrons under strong magnetic fields1,2. Recently, it was shown that an appropriate strain texture in graphene could induce a synthetic gauge field3,4,5,6, in which electrons behave as they do in a real magnetic field7,8,9,10,11. This enabled the control of quantum transport by mechanical means and allowed the unreached high-field regime to be explored. Such synthetic gauge fields have been achieved in molecular12 and photonic13 lattices. Here we report an experimental realization of a giant uniform pseudomagnetic field in acoustics by introducing a simple uniaxial deformation to the acoustic graphene. The controllability of our macroscopic platform enables us to observe the acoustic Landau levels in frequency-resolved spectroscopy and their spatial localization in pressure-field distributions. We further visualize the quantum-Hall-like edge states (connected to the zeroth Landau level), which have been elusive owing to the difficulty in creating large-area uniform pseudomagnetic fields5,6. These results, consistent with our full-wave simulations, establish a complete framework for artificial structures under constant pseudomagnetic fields. Our findings may also offer opportunities to manipulate sound in conceptually novel ways.

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Fig. 1: Synthesized acoustic magnetic field and relativistic Landau quantization.
Fig. 2: Experimental detection of the acoustic Landau quantization.
Fig. 3: Acoustic quantum-Hall-like edge states generated by the effective magnetic field.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

    Article  ADS  Google Scholar 

  2. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & denNijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  ADS  Google Scholar 

  3. Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30–33 (2010).

    Article  Google Scholar 

  4. Low, T. & Guinea, F. Strain-induced pseudomagnetic field for novel graphene electronics. Nano. Lett. 10, 3551–3554 (2010).

    Article  ADS  Google Scholar 

  5. Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 Tesla in graphene nanobubbles. Science 329, 544–547 (2010).

    Article  ADS  Google Scholar 

  6. Lu, J., Neto, A. H. C. & Loh, K. P. Transforming moiré blisters into geometric graphene nano-bubbles. Nat. Commun. 3, 823 (2012).

    Article  ADS  Google Scholar 

  7. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  ADS  Google Scholar 

  8. Zhang, Y., Tan, Y., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  ADS  Google Scholar 

  9. Novoselov, K. S. et al. Room temperature quantum Hall effect in graphene. Science 315, 1379–1379 (2007).

    Article  ADS  Google Scholar 

  10. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  ADS  Google Scholar 

  11. Goerbig, M. O. Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 83, 1193–1423 (2011).

    Article  ADS  Google Scholar 

  12. Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

    Article  ADS  Google Scholar 

  13. Rechtsman, M. C. et al. Strain-induced pseudomagnetic field and photonic landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013).

    Article  ADS  Google Scholar 

  14. Schomerus, H. & Halpern, N. Y. Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices. Phys. Rev. Lett. 110, 013903 (2013).

    Article  ADS  Google Scholar 

  15. Brendel, C., Peano, V., Painter, O. J. & Marquardt, F. Pseudomagnetic fields for sound at the nanoscale. Proc. Natl Acad. Sci. USA 114, E3390–E3395 (2017).

    Article  ADS  Google Scholar 

  16. Abbaszadeh, H., Souslov, A., Paulose, J., Schomerus, H. & Vitelli, V. Sonic Landau levels and synthetic gauge fields in mechanical metamaterials. Phys. Rev. Lett. 119, 195502 (2017).

  17. Yang, Z., Gao, F., Yang, Y. & Zhang, B. Strain-induced gauge field and Landau levels in acoustic structures. Phys. Rev. Lett. 118, 194301 (2017).

    Article  ADS  Google Scholar 

  18. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

    Article  ADS  Google Scholar 

  19. Rechtsman, M. C. et al. Photonic floquet topological insulators. Nature 496, 196–200 (2013).

    Article  ADS  Google Scholar 

  20. Susstrunk, R. & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).

    Article  ADS  Google Scholar 

  21. Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  22. Xiao, M. et al. Geometric phase and band inversion in periodic acoustic systems. Nat. Phys. 11, 240–244 (2015).

    Article  Google Scholar 

  23. He, C. et al. Acoustic topological insulator and robust one-way sound transport. Nat. Phys. 12, 1124–1129 (2016).

    Article  Google Scholar 

  24. Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator. Nature 555, 342–345 (2018).

    Article  ADS  Google Scholar 

  25. Peterson, C. W., Benalcazar, W. A., Hughes, T. L. & Bahl, G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555, 346–350 (2018).

    Article  ADS  Google Scholar 

  26. Halperin, B. I. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185–2190 (1982).

    Article  ADS  Google Scholar 

  27. Li, F., Huang, X., Lu, J., Ma, J. & Liu, Z. Weyl points and Fermi arcs in a chiral phononic crystal. Nat. Phys. 14, 30–34 (2018).

    Article  Google Scholar 

  28. He, H. et al. Topological negative refraction of surface acoustic waves in a Weyl phononic crystal. Nature 560, 61–64 (2018).

    Article  ADS  Google Scholar 

  29. Ge, H. et al. Experimental observation of acoustic Weyl points and topological surface states. Phys. Rev. Appl. 10, 014017 (2018).

    Article  ADS  Google Scholar 

  30. Lu, J. et al. Observation of topological valley transport of sound in sonic crystals. Nat. Phys. 13, 369–374 (2017).

    Article  Google Scholar 

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This work is supported by the National Basic Research Program of China (grant number 2015CB755500); the National Natural Science Foundation of China (grant numbers 11774275, 11674250, 11534013, 11747310 and 11890701); the National Key R&D Program of China (grant number 2018FYA0305800); the Natural Science Foundation of Hubei Province (grant number 2017CFA042). F.Z. was supported by University of Texas at Dallas research enhancement funds and the Army Research Office under grant number W911NF-18-1-0416.

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Authors and Affiliations



C.Q. conceived the idea and supervised the project. X.W. performed the simulations. X.W., Y.Q. and L.Y. did the experiments. C.Q., X.W., F.Z. and Z.L. analysed the data and wrote the manuscript. All authors contributed to scientific discussion of the manuscript.

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Correspondence to Chunyin Qiu.

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Supplementary Figures 1–6.

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Wen, X., Qiu, C., Qi, Y. et al. Acoustic Landau quantization and quantum-Hall-like edge states. Nat. Phys. 15, 352–356 (2019).

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