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Multiple and spectrally robust photonic magic angles in reconfigurable α-MoO3 trilayers

Abstract

The emergence of a topological transition of the polaritonic dispersion in twisted bilayers of anisotropic van der Waals materials at a given twist angle—the photonic magic angle—results in the diffractionless propagation of polaritons with deep-subwavelength resolution. This type of propagation, generally referred to as canalization, holds promise for the control of light at the nanoscale. However, the existence of a single photonic magic angle hinders such control since the canalization direction in twisted bilayers is unique and fixed for each incident frequency. Here we overcome this limitation by demonstrating multiple spectrally robust photonic magic angles in reconfigurable twisted α-phase molybdenum trioxide (α-MoO3) trilayers. We show that canalization of polaritons can be programmed at will along any desired in-plane direction in a single device with broad spectral ranges. These findings open the door for nanophotonics applications where on-demand control is crucial, such as thermal management, nanoimaging or entanglement of quantum emitters.

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Fig. 1: Photonic magic angles and polariton canalization in reconfigurable trilayers.
Fig. 2: Multiple photonic magic angles and all-angle tunable polariton canalization in twisted trilayers.
Fig. 3: Experimental demonstration of multiple photonic magic angles and tunable polariton canalization in twisted trilayers.
Fig. 4: Spectrally robust photonic magic angles and broadband polariton canalization in twisted trilayers.

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

References

  1. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  Google Scholar 

  2. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).

    Article  CAS  Google Scholar 

  3. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    Article  CAS  Google Scholar 

  4. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).

    Article  CAS  Google Scholar 

  5. Ponomarenko, L. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    Article  CAS  Google Scholar 

  6. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  CAS  Google Scholar 

  7. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  CAS  Google Scholar 

  8. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

    Article  CAS  Google Scholar 

  9. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

    Article  CAS  Google Scholar 

  10. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).

    Article  CAS  Google Scholar 

  11. Hesp, N. C. et al. Observation of interband collective excitations in twisted bilayer graphene. Nat. Phys. 17, 1162–1168 (2021).

    Article  CAS  Google Scholar 

  12. Sunku, S. S. et al. Hyperbolic enhancement of photocurrent patterns in minimally twisted bilayer graphene. Nat. Commun. 12, 1641 (2021).

    Article  CAS  Google Scholar 

  13. Hesp, N. C. et al. Nano-imaging photoresponse in a moiré unit cell of minimally twisted bilayer graphene. Nat. Commun. 12, 1640 (2021).

    Article  CAS  Google Scholar 

  14. Sunku, S. et al. Photonic crystals for nano-light in moiré graphene superlattices. Science 362, 1153–1156 (2018).

    Article  CAS  Google Scholar 

  15. Hu, G., Krasnok, A., Mazor, Y., Qiu, C.-W. & Alù, A. Moiré hyperbolic metasurfaces. Nano Lett. 20, 3217–3224 (2020).

    Article  CAS  Google Scholar 

  16. Hu, G. et al. Topological polaritons and photonic magic angles in twisted α-MoO3 bilayers. Nature 582, 209–213 (2020).

    Article  CAS  Google Scholar 

  17. Chen, M. et al. Configurable phonon polaritons in twisted α-MoO3. Nat. Mater. 19, 1307–1311 (2020).

    Article  CAS  Google Scholar 

  18. Duan, J. et al. Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs. Nano Lett. 20, 5323–5329 (2020).

    Article  CAS  Google Scholar 

  19. Zheng, Z. et al. Phonon polaritons in twisted double-layers of hyperbolic van der Waals crystals. Nano Lett. 20, 5301–5308 (2020).

    Article  CAS  Google Scholar 

  20. Herzig Sheinfux, H. & Koppens, F. H. The rise of twist-optics. Nano Lett. 20, 6935–6936 (2020).

    Article  CAS  Google Scholar 

  21. Basov, D., Fogler, M. & García de Abajo, F. Polaritons in van der Waals materials. Science 354, aag1992 (2016).

    Article  Google Scholar 

  22. Low, T. et al. Polaritons in layered two-dimensional materials. Nat. Mater. 16, 182–194 (2017).

    Article  CAS  Google Scholar 

  23. Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons. Nanophotonics 4, 44–68 (2015).

    Article  CAS  Google Scholar 

  24. Li, P. et al. Collective near-field coupling and nonlocal phenomena in infrared-phononic metasurfaces for nano-light canalization. Nat. Commun. 11, 3663 (2020).

    Article  CAS  Google Scholar 

  25. Gomez-Diaz, J. S., Tymchenko, M. & Alu, A. Hyperbolic plasmons and topological transitions over uniaxial metasurfaces. Phys. Rev. Lett. 114, 233901 (2015).

    Article  Google Scholar 

  26. Krishnamoorthy, H. N., Jacob, Z., Narimanov, E., Kretzschmar, I. & Menon, V. M. Topological transitions in metamaterials. Science 336, 205–209 (2012).

    Article  CAS  Google Scholar 

  27. Zhang, Q. et al. Interface nano-optics with van der Waals polaritons. Nature 597, 187–195 (2021).

    Article  CAS  Google Scholar 

  28. Tomarken, S. L. et al. Electronic compressibility of magic-angle graphene superlattices. Phys. Rev. Lett. 123, 046601 (2019).

    Article  CAS  Google Scholar 

  29. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    Article  CAS  Google Scholar 

  30. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  CAS  Google Scholar 

  31. Rubio-Verdú, C. et al. Moiré nematic phase in twisted double bilayer graphene. Nat. Phys. 18, 196–202 (2022).

    Article  Google Scholar 

  32. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).

    Article  CAS  Google Scholar 

  33. Ma, W. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal. Nature 562, 557–562 (2018).

    Article  CAS  Google Scholar 

  34. Zheng, Z. et al. A mid-infrared biaxial hyperbolic van der Waals crystal. Sci. Adv. 5, eaav8690 (2019).

    Article  CAS  Google Scholar 

  35. Álvarez‐Pérez, G. et al. Infrared permittivity of the biaxial van der waals semiconductor α‐MoO3 from near‐and far‐field correlative studies. Adv. Mater. 32, 1908176 (2020).

    Article  Google Scholar 

  36. Alonso-González, P. et al. Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns. Science 344, 1369–1373 (2014).

    Article  Google Scholar 

  37. Pons-Valencia, P. et al. Launching of hyperbolic phonon-polaritons in h-BN slabs by resonant metal plasmonic antennas. Nat. Commun. 10, 3242 (2019).

    Article  CAS  Google Scholar 

  38. Passler, N. C. et al. Hyperbolic shear polaritons in low-symmetry crystals. Nature 602, 595–600 (2022).

    Article  CAS  Google Scholar 

  39. Hu, G. et al. Real-space nanoimaging of hyperbolic shear polaritons in a monoclinic crystal. Nat. Nanotechnol. 18, 64–70 (2023).

    Article  CAS  Google Scholar 

  40. Taboada-Gutiérrez, J. et al. Broad spectral tuning of ultra-low-loss polaritons in a van der Waals crystal by intercalation. Nat. Mater. 19, 964–968 (2020).

    Article  Google Scholar 

  41. Wang, C. et al. Van der Waals thin films of WTe2 for natural hyperbolic plasmonic surfaces. Nat. Commun. 11, 1158 (2020).

    Article  CAS  Google Scholar 

  42. Álvarez-Pérez, G. et al. Active tuning of highly anisotropic phonon polaritons in van der Waals crystal slabs by gated graphene. ACS Photonics 9, 383–390 (2022).

    Article  Google Scholar 

  43. Bapat, A. et al. Gate tunable light–matter interaction in natural biaxial hyperbolic van der Waals heterostructures. Nanophotonics 11, 2329–2340 (2022).

    Article  CAS  Google Scholar 

  44. Ruta, F. L. et al. Surface plasmons induce topological transition in graphene/α-MoO3 heterostructures. Nat. Commun. 13, 3719 (2022).

    Article  CAS  Google Scholar 

  45. Zeng, Y. et al. Tailoring topological transition of anisotropic polaritons by interface engineering in biaxial crystals. Nano Lett. 22, 4260–4268 (2022).

    Article  CAS  Google Scholar 

  46. Hu, H. et al. Doping-driven topological polaritons in graphene/α-MoO3 heterostructures. Nat. Nanotechnol. 17, 940–946 (2022).

    Article  CAS  Google Scholar 

  47. Ma, W. et al. Deep learning for the design of photonic structures. Nat. Photon. 15, 77–90 (2021).

    Article  CAS  Google Scholar 

  48. Kudyshev, Z. A. et al. Machine learning–assisted global optimization of photonic devices. Nanophotonics 10, 371–383 (2021).

    Article  Google Scholar 

  49. He, M. et al. Deterministic inverse design of Tamm plasmon thermal emitters with multi-resonant control. Nat. Mater. 20, 1663–1669 (2021).

    Article  CAS  Google Scholar 

  50. Wiecha, P. R. et al. Deep learning in nano-photonics: inverse design and beyond. Photon. Res. 9, B182–B200 (2021).

    Article  Google Scholar 

  51. Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).

    Article  CAS  Google Scholar 

  52. Frisenda, R. et al. Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials. Chem. Soc. Rev. 47, 53–68 (2018).

    Article  CAS  Google Scholar 

  53. Aguilar-Merino, P. et al. Extracting the infrared permittivity of SiO2 substrates locally by near-field imaging of phonon polaritons in a van der Waals crystal. Nanomaterials 11, 120 (2021).

    Article  CAS  Google Scholar 

  54. Passler, N. C. & Paarmann, A. Generalized 4 × 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures. J. Opt. Soc. Am. B 34, 2128–2139 (2017).

    Article  CAS  Google Scholar 

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Acknowledgements

A.I.F.T.-M. and G.Á.-P. acknowledge support from the Severo Ochoa program of the Government of the Principality of Asturias (nos. PA-21-PF-BP20-117 and PA-20-PF-BP19-053, respectively). J.M.-S. acknowledges financial support from the Ramón y Cajal Program of the Government of Spain and FSE (RYC2018-026196-I) and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant no. PID2019-110308GA-I00). P.A.-G. acknowledges support from the European Research Council under starting grant no. 715496, 2DNANOPTICA and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant no. PID2019-111156GB-I00). A.Y.N. acknowledges the Spanish Ministry of Science and Innovation (grant PID2020-115221GB-C42) and the Basque Department of Education (grant PIBA-2020-1-0014). This project has also been supported by Asturias FICYT under grant AYUD/2021/51185 with the support of FEDER funds. These results also received support from a fellowship from ‘la Caixa’ Foundation (ID 100010434). The fellowship code is LCF/BQ/DI21/11860026. In addition, this work was supported by a 2022 Leonardo Grant for Researchers in Physics, BBVA Foundation. The foundation takes no responsibility for the opinions, statements and contents of this project, which are entirely the responsibility of its authors.

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J.D. and P.A.-G. conceived the study. P.A.-G. and A.Y.N. supervised the project. J.D. and A.I.F.T-M. fabricated the twisted samples. J.D. carried out the near-field imaging experiments. C.L., K.V. and G.Á.-P. carried out the numerical simulations and analytical calculations with the help of N.C.-R. and A.T.M.-L. J.D., P.A.-G., A.Y.N., J.M.-S., V.S.V. and G.Á.-P. participated in the data analysis. J.D., P.A.-G., G.Á.-P. and C.L. co-wrote the manuscript with input from the rest of the authors.

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Correspondence to J. Duan, A. Y. Nikitin or P. Alonso-González.

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Duan, J., Álvarez-Pérez, G., Lanza, C. et al. Multiple and spectrally robust photonic magic angles in reconfigurable α-MoO3 trilayers. Nat. Mater. 22, 867–872 (2023). https://doi.org/10.1038/s41563-023-01582-5

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