Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Perspective
  • Published:

Engineered moiré photonic and phononic superlattices

Nature Materials volume 23, pages 1169–1178 (2024)Cite this article

Subjects

Abstract

Recent discoveries of Mott insulating and unconventional superconducting states in twisted bilayer graphene with moiré superlattices have not only reshaped the landscape of ‘twistronics’ but also sparked the rapidly growing fields of moiré photonic and phononic structures. These innovative moiré structures have opened new routes of exploration for classical wave physics, leading to intriguing phenomena and robust control of electromagnetic and mechanical waves. Drawing inspiration from the success of twisted bilayer graphene, this Perspective describes an overarching framework of the emerging moiré photonic and phononic structures that promise novel classical wave devices. We begin with the fundamentals of moiré superlattices, before highlighting recent studies that exploit twist angle and interlayer coupling as new ingredients with which to engineer and tailor the band structures and effective material properties of photonic and phononic structures. Finally, we discuss the future directions and prospects of this emerging area in materials science and wave physics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Examples of moiré photonic structures.
Fig. 2: Examples of moiré phononic structures.

Similar content being viewed by others

References

  1. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  CAS  PubMed  Google Scholar 

  2. Carr, S. et al. Twistronics: manipulating the electronic properties of two-dimensional layered structures through their twist angle. Phys. Rev. B 95, 075420 (2017).

    Article  Google Scholar 

  3. Rozhkov, A. V., Sboychakov, A. O., Rakhmanov, A. L. & Nori, F. Electronic properties of graphene-based bilayer systems. Phys. Rep. 648, 1–104 (2016).

    Article  CAS  Google Scholar 

  4. Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).

    Article  Google Scholar 

  5. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  7. Moon, P. & Koshino, M. Optical absorption in twisted bilayer graphene. Phys. Rev. B 87, 205404 (2013).

    Article  Google Scholar 

  8. Li, H. et al. Thermal conductivity of twisted bilayer graphene. Nanoscale 6, 13402–13408 (2014).

    Article  CAS  PubMed  Google Scholar 

  9. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  11. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  13. Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).

    CAS  Google Scholar 

  14. Deng, Y. et al. Magic-angle bilayer phononic graphene. Phys. Rev. B 102, 180304(R) (2020).

    Article  Google Scholar 

  15. Rosendo López, M., Peñaranda, F., Christensen, J. & San-Jose, P. Flat bands in magic-angle vibrating plates. Phys. Rev. Lett. 125, 214301 (2020).

    Article  PubMed  Google Scholar 

  16. Oudich, M. et al. Photonic analog of bilayer graphene. Phys. Rev. B 103, 214311 (2021).

    Article  CAS  Google Scholar 

  17. Gardezi, S. M., Pirie, H., Carr, S., Dorrell, W. & Hoffman, J. E. Simulating twistronics in acoustic metamaterials. 2D Mater. 8, 031002 (2021).

    Article  CAS  Google Scholar 

  18. Tang, H. et al. Modeling the optical properties of twisted bilayer photonic crystals. Light Sci. Appl. 10, 157 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Dong, K. et al. Flat bands in magic-angle bilayer photonic crystals at small twists. Phys. Rev. Lett. 126, 223601 (2021).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  21. Du, L. et al. Moiré photonics and optoelectronics. Science 379, eadg0014 (2023).

    Article  CAS  PubMed  Google Scholar 

  22. Correas-Serrano, D., Gomez-Diaz, J. S., Melcon, A. A. & Alù, A. Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization. J. Opt. 18, 104006 (2016).

    Article  Google Scholar 

  23. Dai, Z. et al. Edge-oriented and steerable hyperbolic polaritons in anisotropic van der Waals nanocavities. Nat. Commun. 11, 6086 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  27. Gomez-Diaz, J. S. & Alù, A. Flatland optics with hyperbolic metasurfaces. ACS Photonics 3, 2211–2224 (2016).

    Article  CAS  Google Scholar 

  28. Kotov, O. V. & Lozovik, Yu. E. Hyperbolic hybrid waves and optical topological transitions in few-layer anisotropic metasurfaces. Phys. Rev. B 100, 165424 (2019).

    Article  CAS  Google Scholar 

  29. Hu, G., Zheng, C., Ni, J., Qiu, C.-W. & Alù, A. Enhanced light–matter interactions at photonic magic-angle topological transitions. Appl. Phys. Lett. 118, 211101 (2021).

    Article  CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  31. Zhang, X., Zhong, Y., Low, T., Chen, H. & Lin, X. Emerging chiral optics from chiral interfaces. Phys. Rev. B 103, 195405 (2021).

    Article  CAS  Google Scholar 

  32. Stauber, T., Low, T. & Gómez-Santos, G. Chiral response of twisted bilayer graphene. Phys. Rev. Lett. 120, 046801 (2018).

    Article  CAS  PubMed  Google Scholar 

  33. Wu, B.-Y., Shi, Z.-X., Wu, F., Wang, M.-J. & Wu, X.-H. Strong chirality in twisted bilayer α-MoO3. Chin. Phys. B 31, 044101 (2022).

    Article  CAS  Google Scholar 

  34. Lin, X. et al. Chiral plasmons with twisted atomic bilayers. Phys. Rev. Lett. 125, 077401 (2020).

    Article  CAS  PubMed  Google Scholar 

  35. Wang, J., Bo, W., Ding, Y., Wang, X. & Mu, X. Optical, optoelectronic, and photoelectric properties in moiré superlattices of twist bilayer graphene. Mater. Today Phys. 14, 100238 (2020).

    Article  Google Scholar 

  36. Mao, X.-R., Shao, Z.-K., Luan, H.-Y., Wang, S.-L. & Ma, R.-M. Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol. 16, 1099–1105 (2021).

    Article  CAS  PubMed  Google Scholar 

  37. Wang, H., Ma, S., Zhang, S. & Lei, D. Intrinsic superflat bands in general twisted bilayer systems. Light Sci. Appl. 11, 159 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Garcia-Vidal, F. J. et al. Spoof surface plasmon photonics. Rev. Mod. Phys. 94, 025004 (2022).

    Article  Google Scholar 

  39. Gao, Z. et al. Valley surface-wave photonic crystal and its bulk/edge transport. Phys. Rev. B 96, 201402 (2017).

    Article  Google Scholar 

  40. Lou, B. et al. Theory for twisted bilayer photonic crystal slabs. Phys. Rev. Lett. 126, 136101 (2021).

    Article  CAS  PubMed  Google Scholar 

  41. Huang, L., Zhang, W. & Zhang, X. Moiré quasibound states in the continuum. Phys. Rev. Lett. 128, 253901 (2022).

    Article  CAS  PubMed  Google Scholar 

  42. Lou, B., Wang, B., Rodríguez, J. A., Cappelli, M. & Fan, S. Tunable guided resonance in twisted bilayer photonic crystal. Sci. Adv. 8, eadd4339 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Lou, B. & Fan, S. Tunable frequency filter based on twisted bilayer photonic crystal slabs. ACS Photon. 9, 800–805 (2022).

    Article  CAS  Google Scholar 

  44. Yi, C.-H., Park, H. C. & Park, M. J. Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices. Light Sci. Appl. 11, 289 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Wang, P. et al. Localization and delocalization of light in photonic moiré lattices. Nature 577, 42–46 (2020).

    Article  CAS  PubMed  Google Scholar 

  46. Mahmood, R., Ramirez, A. V. & Hillier, A. C. Creating two-dimensional quasicrystal, supercell, and Moiré lattices with laser interference lithography: implications for photonic bandgap materials. ACS Appl. Nano Mater. 4, 8851–8862 (2021).

    Article  CAS  Google Scholar 

  47. Lubin, S. M., Hryn, A. J., Huntington, M. D., Engel, C. J. & Odom, T. W. Quasiperiodic moiré plasmonic crystals. ACS Nano 7, 11035–11042 (2013).

    Article  CAS  PubMed  Google Scholar 

  48. Zhang, Y. et al. Unfolded band structures of photonic quasicrystals and moiré superlattices. Phys. Rev. B 105, 165304 (2022).

    Article  CAS  Google Scholar 

  49. Guan, J. et al. Far-field coupling between moiré photonic lattices. Nat. Nanotechnol. 18, 514–520 (2023).

    Article  CAS  PubMed  Google Scholar 

  50. Wang, W. et al. Moiré fringe induced gauge field in photonics. Phys. Rev. Lett. 125, 203901 (2020).

    Article  CAS  PubMed  Google Scholar 

  51. Hong, P. et al. Flatband mode in photonic moiré superlattice for boosting second-harmonic generation with monolayer van der Waals crystals. Opt. Lett. 47, 2326–2329 (2022).

    Article  PubMed  Google Scholar 

  52. Nguyen, H. S. et al. Symmetry breaking in photonic crystals: on-demand dispersion from flatband to Dirac cones. Phys. Rev. Lett. 120, 066102 (2018).

    Article  CAS  PubMed  Google Scholar 

  53. Nguyen, D. X. et al. Magic configurations in moiré superlattice of bilayer photonic crystals: almost-perfect flatbands and unconventional localization. Phys. Rev. Res. 4, L032031 (2022).

    Article  CAS  Google Scholar 

  54. Talukdar, T. H., Hardison, A. L. & Ryckman, J. D. Moiré effects in silicon photonic nanowires. ACS Photon. 9, 1286–1294 (2022).

    Article  CAS  Google Scholar 

  55. Dorrell, W., Pirie, H., Gardezi, S. M., Drucker, N. C. & Hoffman, J. E. van der Waals metamaterials. Phys. Rev. B 101, 121103 (2020).

    Article  CAS  Google Scholar 

  56. Lu, J. et al. Valley topological phases in bilayer sonic crystals. Phys. Rev. Lett. 120, 116802 (2018).

    Article  CAS  PubMed  Google Scholar 

  57. Wu, S.-Q. et al. Higher-order topological states in acoustic twisted moiré superlattices. Phys. Rev. Appl. 17, 034061 (2022).

    Article  CAS  Google Scholar 

  58. López, M. R., Zhang, Z., Torrent, D. & Christensen, J. Theory of holey twistsonic media. Commun. Mater. 3, 99 (2022).

    Article  Google Scholar 

  59. Martí-Sabaté, M. & Torrent, D. Dipolar localization of waves in twisted phononic crystal plates. Phys. Rev. Appl. 15, L011001 (2021).

    Article  Google Scholar 

  60. Oudich, M., Deng, Y. & Jing, Y. Twisted pillared phononic crystal plates. Appl. Phys. Lett. 120, 232202 (2022).

    Article  CAS  Google Scholar 

  61. Yves, S. et al. Moiré-driven topological transitions and extreme anisotropy in elastic metasurfaces. Adv. Sci. 9, 2200181 (2022).

    Article  Google Scholar 

  62. Jin, Y., Wang, W., Wen, Z., Torrent, D. & Djafari-Rouhani, B. Topological states in twisted pillared phononic plates. Extreme Mech. Lett. 39, 100777 (2020).

    Article  Google Scholar 

  63. Tang, L. et al. Photonic flat-band lattices and unconventional light localization. Nanophotonics 9, 1161–1176 (2020).

    Article  Google Scholar 

  64. Wang, H. et al. Exceptional concentric rings in a non-Hermitian bilayer photonic system. Phys. Rev. B 100, 165134 (2019).

    Article  CAS  Google Scholar 

  65. Zhang, D. et al. PT-symmetric non-Hermitian AB-stacked bilayer honeycomb photonic lattice. J. Opt. Soc. Am. B 37, 3407–3413 (2020).

    Article  CAS  Google Scholar 

  66. Wang, D. et al. Realization of a \(\mathbb{Z}\)-classified chiral-symmetric higher-order topological insulator in a coupling-inverted acoustic crystal. Phys. Rev. Lett. 131, 157201 (2023).

  67. Wang, H.-F. et al. Bound states in the continuum in a bilayer photonic crystal with TE–TM cross coupling. Phys. Rev. B 98, 214101 (2018).

    Article  CAS  Google Scholar 

  68. Liu, L., Li, T., Zhang, Q., Xiao, M. & Qiu, C. Universal mirror-stacking approach for constructing topological bound states in the continuum. Phys. Rev. Lett. 130, 106301 (2023).

    Article  CAS  PubMed  Google Scholar 

  69. Di Mauro Villari, L. & Principi, A. Optotwistronics of bilayer graphene. Phys. Rev. B 106, 035401 (2022).

    Article  Google Scholar 

  70. Zhang, Y., Qin, Y., Zheng, H. & Ren, H. The evolution of the solitons in periodic photonic moiré lattices controlled by rotation angle with saturable self-focusing nonlinearity media. Laser Phys. 32, 045401 (2022).

    Article  Google Scholar 

  71. Fang, X., Wen, J., Bonello, B., Yin, J. & Yu, D. Ultra-low and ultra-broad-band nonlinear acoustic metamaterials. Nat. Commun. 8, 1288 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  72. Librandi, G., Tubaldi, E. & Bertoldi, K. Programming nonreciprocity and reversibility in multistable mechanical metamaterials. Nat. Commun. 12, 3454 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Guo, X., Gusev, V. E., Tournat, V., Deng, B. & Bertoldi, K. Frequency-doubling effect in acoustic reflection by a nonlinear, architected rotating-square metasurface. Phys. Rev. E 99, 052209 (2019).

    Article  CAS  PubMed  Google Scholar 

  74. Deng, B., Raney, J. R., Tournat, V. & Bertoldi, K. Elastic vector solitons in soft architected materials. Phys. Rev. Lett. 118, 204102 (2017).

    Article  CAS  PubMed  Google Scholar 

  75. Deng, B., Wang, P., He, Q., Tournat, V. & Bertoldi, K. Metamaterials with amplitude gaps for elastic solitons. Nat. Commun. 9, 3410 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  76. Wang, X. et al. A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems. Front. Optoelectron. 16, 38 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Motycka, J. A grazing-incidence moire interferometer for displacement and planeness measurement. Exp. Mech. 15, 279–281 (1975).

    Article  Google Scholar 

  78. Khan, M. T. I., Kazuhiko, M., Teramoto, K. & Hasan, M. M. Precise measurement of moving object by moiré-based image processing technique. Open J. Fluid Dyn. 2, 202–207 (2012).

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  80. Ikeda, T. N. High-order nonlinear optical response of a twisted bilayer graphene. Phys. Rev. Res. 2, 032015 (2020).

    Article  CAS  Google Scholar 

  81. Katz, O., Refael, G. & Lindner, N. H. Optically induced flat bands in twisted bilayer graphene. Phys. Rev. B 102, 155123 (2020).

    Article  CAS  Google Scholar 

  82. Kort-Kamp, W. J. M., Culchac, F. J., Capaz, R. B. & Pinheiro, F. A. Photonic spin Hall effect in bilayer graphene moiré superlattices. Phys. Rev. B 98, 195431 (2018).

    Article  CAS  Google Scholar 

  83. Polshyn, H. et al. Large linear-in-temperature resistivity in twisted bilayer graphene. Nat. Phys. 15, 1011–1016 (2019).

    Article  CAS  Google Scholar 

  84. Alborzi, M. S., Rajabpour, A. & Montazeri, A. Heat transport in 2D van der Waals heterostructures: an analytical modeling approach. Int. J. Therm. Sci. 150, 106237 (2020).

    Article  Google Scholar 

  85. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  88. Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).

    Article  CAS  PubMed  Google Scholar 

  89. Crasto de Lima, F., Miwa, R. H. & Suárez Morell, E. Double flat bands in kagome twisted bilayers. Phys. Rev. B 100, 155421 (2019).

    Article  CAS  Google Scholar 

  90. Sinha, M. et al. Twisting of 2D kagomé sheets in layered intermetallics. ACS Cent. Sci. 7, 1381–1390 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  91. Can, O. et al. High-temperature topological superconductivity in twisted double-layer copper oxides. Nat. Phys. 17, 519–524 (2021).

    Article  CAS  Google Scholar 

  92. Alnasser, K., Kamau, S., Hurley, N., Cui, J. & Lin, Y. Photonic band gaps and resonance modes in 2D twisted moiré photonic crystal. Photonics 8, 408 (2021).

    Article  Google Scholar 

  93. Zheng, S. et al. Topological network and valley beam splitter in acoustic biaxially strained moiré superlattices. Phys. Rev. B 105, 184104 (2022).

    Article  CAS  Google Scholar 

  94. Tang, H., Ni, X., Du, F., Srikrishna, V. & Mazur, E. On-chip light trapping in bilayer moiré photonic crystal slabs. Appl. Phys. Lett. 121, 231702 (2022).

    Article  CAS  Google Scholar 

  95. Raun, A., Tang, H., Ni, X., Mazur, E. & Hu, E. L. GaN magic angle laser in a merged moiré photonic crystal. ACS Photon. 10, 3001–3007 (2023).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

Y.J. acknowledges the support of the US National Science Foundation (CMMI 2039463). C.Q. acknowledges financial support from the National Research Foundation (grant no. NRF-CRP26-2021-0004) and IRG from A*STAR (grant no. M22K2c0088 with WBS A-8001322-00-00).

Author information

Authors and Affiliations

  1. Graduate Program in Acoustics, Penn State University, University Park, PA, USA

    Mourad Oudich & Yun Jing

  2. Institut Jean Lamour, CNRS, Université de Lorraine, Nancy, France

    Mourad Oudich

  3. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Xianghong Kong, Tan Zhang & Chengwei Qiu

Authors
  1. Mourad Oudich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xianghong Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengwei Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yun Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Chengwei Qiu or Yun Jing.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Oudich, M., Kong, X., Zhang, T. et al. Engineered moiré photonic and phononic superlattices. Nat. Mater. 23, 1169–1178 (2024). https://doi.org/10.1038/s41563-024-01950-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-024-01950-9

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing