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Gigahertz topological valley Hall effect in nanoelectromechanical phononic crystals

Nature Electronics volume 5, pages 157–163 (2022)Cite this article

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Abstract

Topological phononic crystals can manipulate elastic waves that propagate in solids without being backscattered, and could be used to develop integrated acousto-electronic systems for classical and quantum information processing. However, acoustic topological metamaterials have been mainly limited to macroscale systems that operate at low (kilohertz to megahertz) frequencies. Here we report a topological valley Hall effect in nanoelectromechanical aluminium nitride membranes at gigahertz (up to 1.06 GHz) frequencies. We visualize the propagation of elastic waves through phononic crystals with high sensitivity (10–100 fm) and spatial resolution (10–100 nm) using transmission-mode microwave impedance microscopy. The valley Hall edge states, which are protected by band topology, are observed in both real and momentum space. Robust valley-polarized transport is evident from wave transmission across local disorder and around sharp corners. We also show that the system can be used to create an acoustic beamsplitter.

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Fig. 1: Phononic crystal design and calculated band structures.
Fig. 2: Characterization of gapless and gapped phononic crystals.
Fig. 3: Real-space imaging and momentum-space analysis of valley Hall edge states.
Fig. 4: Robustness of valley Hall edge transport.
Fig. 5: Demonstration of topological beamsplitting.

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Data availability

The raw data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

    Article  Google Scholar 

  2. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045 (2010).

    Article  Google Scholar 

  3. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Nash, L. M. et al. Topological mechanics of gyroscopic metamaterials. Proc. Natl Acad. Sci. USA 112, 14495–14500 (2015).

    Article  Google Scholar 

  6. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

    Article  Google Scholar 

  7. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  MathSciNet  Google Scholar 

  8. Ma, G., Xiao, M. & Chan, C. T. Topological phases in acoustic and mechanical systems. Nat. Rev. Phys. 1, 281–294 (2019).

    Google Scholar 

  9. Liu, Y., Chen, X. & Xu, Y. Topological phononics: from fundamental models to real materials. Adv. Funct. Mater. 30, 1904784 (2020).

    Article  Google Scholar 

  10. Khanikaev, A. B., Fleury, R., Mousavi, S. H. & Alu, A. Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015).

    Article  Google Scholar 

  11. Mousavi, S. H., Khanikaev, A. B. & Wang, Z. Topologically protected elastic waves in phononic metamaterials. Nat. Commun. 6, 8682 (2015).

    Article  Google Scholar 

  12. Yang, Z. et al. Topological acoustics. Phys. Rev. Lett. 114, 114301 (2015).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Zhang, Z., Tian, Y., Cheng, Liu, X. & Christensen, J. Experimental verification of acoustic pseudospin multipoles in a symmetry-broken snowflakelike topological insulator. Phys. Rev. B 96, 241306(R) (2017).

    Article  Google Scholar 

  16. Cha, J., Kim, K. W. & Daraio, C. Experimental realization of on-chip topological nanoelectromechanical metamaterials. Nature 564, 229–233 (2018).

    Article  Google Scholar 

  17. Yan, M. et al. On-chip valley topological materials for elastic wave manipulation. Nat. Mater. 17, 993–998 (2018).

    Article  Google Scholar 

  18. Han, X. et al. Experimental demonstration of acoustic valley Hall topological insulators with the robust selection of C3v-symmetric scatterers. Phys. Rev. Appl. 12, 014046 (2019).

    Article  Google Scholar 

  19. Yan, M. et al. Pseudomagnetic fields enabled manipulation of on-chip elastic waves. Phys. Rev. Lett. 127, 136401 (2021).

    Article  Google Scholar 

  20. Ma, J., Xi, X. & Sun, X. Experimental demonstration of dual-band nano-electromechanical valley-Hall topological metamaterials. Adv. Mater. 33, 2006521 (2021).

    Article  Google Scholar 

  21. Cummer, S. A., Christensen, J. & Alu, A. Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1, 16001 (2016).

    Article  Google Scholar 

  22. Hashimoto, K.-Y. Surface Acoustic Wave Devices in Telecommunications: Modelling and Simulation (Springer, 2000).

  23. Ballantine Jr, D. et al. Acoustic Wave Sensors: Theory, Design and Physico-Chemical Applications (Elsevier, 1996).

  24. Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).

    Article  MathSciNet  Google Scholar 

  25. Zheng, L., Wu, D., Wu, X. & Lai, K. Visualization of surface-acoustic-wave potential by transmission-mode microwave impedance microscopy. Phys. Rev. Appl. 9, 061002 (2018).

    Article  Google Scholar 

  26. Zheng, L., Shao, L., Loncar, M. & Lai, K. Imaging acoustic waves by microwave microscopy. IEEE Microw. Mag. 21, 60–71 (2020).

    Article  Google Scholar 

  27. Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2 transistors. Science 344, 1489–1492 (2014).

    Article  Google Scholar 

  28. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    Article  Google Scholar 

  29. 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  Google Scholar 

  30. Brendel, C., Peano, V., Painter, O. J. & Marquardt, F. Snowflake phononic topological insulator at the nanoscale. Phys. Rev. B 97, 020102(R) (2018).

    Article  Google Scholar 

  31. Gorisse, M. et al. Observation of band gaps in the gigahertz range and deaf bands in a hypersonic aluminum nitride phononic crystal slab. Appl. Phys. Lett. 98, 234103 (2011).

    Article  Google Scholar 

  32. Ghasemi Baboly, M., Alaie, S., Reinke, C. M., El-Kady, I. & Leseman, Z. C. Ultra-high frequency, high Q/volume micromechanical resonators in a planar AlN phononic crystal. J. Appl. Phys. 120, 034502 (2016).

    Article  Google Scholar 

  33. Ye, L. et al. Observation of acoustic valley vortex states and valley-chirality locked beam splitting. Phys. Rev. B 95, 174106 (2017).

    Article  Google Scholar 

  34. Vila, J., Pal, R. K. & Ruzzene, M. Observation of topological valley modes in an elastic hexagonal lattice. Phys. Rev. B 96, 134307 (2017).

    Article  Google Scholar 

  35. Wang, M., Ye, L., Christensen, J. & Liu, Z. Valley physics in non-Hermitian artificial acoustic boron nitride. Phys. Rev. Lett. 120, 246601 (2018).

    Article  Google Scholar 

  36. Colombo, L. et al. Investigation of 20% scandium-doped aluminum nitride films for MEMS laterally vibrating resonators. In 2017 IEEE International Ultrasonics Symposium (IUS) 1–4 (IEEE, 2017).

  37. Yang, Y. et al. Batch-fabricated cantilever probes with electrical shielding for nanoscale dielectric and conductivity imaging. J. Micromech. Microeng. 22, 115040 (2012).

    Article  Google Scholar 

  38. Lee, D. et al. Direct visualization of gigahertz acoustic wave propagation in suspended phononic circuits. Phys. Rev. Appl. 16, 034047 (2021).

    Article  Google Scholar 

  39. PICOSCALE Vibrometer System Controller PV-CTRL-V1.0. https://www.smaract.com/controllers-accessories/product/picoscale-vibrometer?download=files/media/categories/Optical%20Metrology/Spec-Sheets/PV-SS_CTRL-V1.0_SpecSheet.pdf (SmarAct, 2021).

  40. Ultra High Frequency and Full-Field Vibration Analysis Performance Testing of Microsystems: Application Note. https://www.polytec.com/fileadmin/website/vibrometry/pdf/OM_AN_VIB_U_003_UHF_Scanning_E_42426.pdf (Polytec, 2016).

  41. Kittel, C. Introduction to Solid State Physics (John Wiley & Sons, 2005).

  42. Wang, Z. et al. Multichannel topological transport in an acoustic valley Hall insulator. Phys. Rev. Appl. 15, 024019 (2021).

    Article  Google Scholar 

  43. Gerfers, F. et al. Sputtered AlN thin films for piezoelectric MEMS devices—FBAR resonators and accelerometers. in Solid State Circuits Technologies (ed Swart, J. W.) Ch. 17 (IntechOpen, 2010).

Download references

Acknowledgements

A.T.C.J., Q.Z. and Z.G. acknowledge support by the NSF through the Laboratory for Research on the Structure of Matter, an NSF Materials Research Science & Engineering Center (MRSEC; DMR-1720530). K.L., D.L., L.Z., X.M. and S.I.M. acknowledge support by the NSF’s Division of Materials Research award DMR-2004536 and Welch Foundation grant F-1814 for the TMIM work. Data analysis was partially supported by the NSF through the Center for Dynamics and Control of Materials, an NSF MRSEC under Cooperative Agreement DMR-1720595. This work was carried out in part at the Singh Center for Nanotechnology, which is supported by the NSF National Nanotechnology Coordinated Infrastructure Program under grant NNCI-2025608. B.Z. and L.H. acknowledge support for the metamaterial design and simulation work by the US Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection and grant N00014-21-1-2703. H.Y. acknowledges support of the National Natural Science Foundation of China (grant no. 11974003). We would like to express our appreciation for useful discussions with T. Olsson and Q. Niu.

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Author notes

  1. These authors contributed equally: Qicheng Zhang, Daehun Lee.

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA

    Qicheng Zhang, Li He, Bo Zhen & A. T. Charlie Johnson

  2. Department of Physics, University of Texas at Austin, Austin, TX, USA

    Daehun Lee, Lu Zheng, Xuejian Ma, Shawn I. Meyer & Keji Lai

  3. State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China

    Han Ye

  4. Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA, USA

    Ze Gong & A. T. Charlie Johnson

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Contributions

A.T.C.J. and K.L. conceived the project. Q.Z. fabricated the phononic devices and performed the band-structure simulations. D.L. and L.Z. performed the TMIM imaging and data analysis. X.M. and S.I.M. contributed to the TMIM data analysis. L.H., Z.G., H.Y. and B.Z. contributed to the phononic crystal design. Q.Z., D.L. and K.L. drafted the manuscript with contributions from all the authors. All the authors have given approval to the final version of the manuscript.

Corresponding authors

Correspondence to Keji Lai or A. T. Charlie Johnson.

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Nature Electronics thanks Yan-Feng Chen, Zhengyou Liu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–5 and Sections 1–5.

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Zhang, Q., Lee, D., Zheng, L. et al. Gigahertz topological valley Hall effect in nanoelectromechanical phononic crystals. Nat Electron 5, 157–163 (2022). https://doi.org/10.1038/s41928-022-00732-y

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