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Optical soliton formation controlled by angle twisting in photonic moiré lattices


Exploration of the impact of synthetic material landscapes featuring tunable geometrical properties on physical processes is a research direction that is currently of great interest because of the outstanding phenomena that are continually being uncovered. Twistronics and the properties of wave excitations in moiré lattices are salient examples. Moiré patterns bridge the gap between aperiodic structures and perfect crystals, thus opening the door to the exploration of effects accompanying the transition from commensurate to incommensurate phases. Moiré patterns have revealed profound effects in graphene-based systems1,2,3,4,5, they are used to manipulate ultracold atoms6,7 and to create gauge potentials8, and are observed in colloidal clusters9. Recently, it was shown that photonic moiré lattices enable observation of the two-dimensional localization-to-delocalization transition of light in purely linear systems10,11. Here, we employ moiré lattices optically induced in photorefractive nonlinear media12,13,14 to elucidate the formation of optical solitons under different geometrical conditions controlled by the twisting angle between the constitutive sublattices. We observe the formation of solitons in lattices that smoothly transition from fully periodic geometries to aperiodic ones, with threshold properties that are a pristine direct manifestation of flat-band physics11.

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Fig. 1: Moiré patterns and properties of their linear eigenmodes.
Fig. 2: Families of 2D solitons in moiré lattices.
Fig. 3: Thresholds for soliton formation in moiré lattices.
Fig. 4: Soliton formation above the linear localization–delocalization threshold.
Fig. 5: Soliton formation below the linear localization–delocalization threshold.

Data availability

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

Code availability

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


  1. 1.

    Decker, R. et al. Local electronic properties of graphene on a BN substrate via scanning tunneling microscopy. Nano Lett. 11, 2291–2295 (2011).

    ADS  Article  Google Scholar 

  2. 2.

    Woods, C. R. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).

    Article  Google Scholar 

  3. 3.

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

    ADS  Article  Google Scholar 

  4. 4.

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

    ADS  Article  Google Scholar 

  5. 5.

    Ahn, S. J. et al. Dirac electrons in a dodecagonal graphene quasicrystal. Science 786, 782–786 (2018).

    ADS  Article  Google Scholar 

  6. 6.

    González-Tudela, A. & Cirac, J. I. Cold atoms in twisted-bilayer optical potentials. Phys. Rev. A 100, 053604 (2019).

    ADS  Article  Google Scholar 

  7. 7.

    Salamon, T. et al. Simulating twistronics without a twist. Phys. Rev. Lett. 125, 030504 (2020).

    ADS  Article  Google Scholar 

  8. 8.

    San-Jose, P., González, J. & Guinea, F. Non-Abelian gauge potentials in graphene bilayers. Phys. Rev. Lett. 108, 216802 (2012).

    ADS  Article  Google Scholar 

  9. 9.

    Cao, X., Panizon, E., Vanossi, A., Manini, N. & Bechinger, C. Orientational and directional locking of colloidal clusters driven across periodic surfaces. Nat. Phys 15, 776–780 (2019).

    Article  Google Scholar 

  10. 10.

    Huang, C. et al. Localization–delocalization wavepacket transition in Pythagorean aperiodic potentials. Sci. Rep. 6, 32546 (2016).

    ADS  Article  Google Scholar 

  11. 11.

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

    ADS  Article  Google Scholar 

  12. 12.

    Efremidis, N. K., Sears, S., Christodoulides, D. N., Fleischer, J. W. & Segev, M. Discrete solitons in photorefractive optically induced photonic lattices. Phys. Rev. E 66, 046602 (2002).

    ADS  Article  Google Scholar 

  13. 13.

    Fleischer, J. W., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003).

    ADS  Article  Google Scholar 

  14. 14.

    Freedman, B. et al. Wave and defect dynamics in nonlinear photonic quasicrystals. Nature 440, 1166–1169 (2006).

    ADS  Article  Google Scholar 

  15. 15.

    Brandes, T. & Kettemann, S. The Anderson Transition and its Ramifications: Localization, Quantum Interference and Interactions (Springer, 2003).

  16. 16.

    Morsch, O. & Oberthaler, M. Dynamics of Bose–Einstein condensates in optical lattices. Rev. Mod. Phys. 78, 179–215 (2006).

    ADS  Article  Google Scholar 

  17. 17.

    Billy, J., Sanchez-Palencia, L., Bouyer, P. & Aspect, A. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

    ADS  Article  Google Scholar 

  18. 18.

    Wiersma, D. S. Disordered photonics. Nat. Photon. 7, 188–196 (2013).

    ADS  Article  Google Scholar 

  19. 19.

    Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).

    ADS  Article  Google Scholar 

  20. 20.

    DasSarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011).

    ADS  Article  Google Scholar 

  21. 21.

    Lederer, F. et al. Discrete solitons in optics. Phys. Rep. 463, 1–126 (2008).

    ADS  Article  Google Scholar 

  22. 22.

    Kartashov, Y. V., Astrakharchik, G., Malomed, B. & Torner, L. Frontiers in multidimensional self-trapping of nonlinear fields and matter. Nat. Rev. Phys. 1, 185–197 (2019).

    Article  Google Scholar 

  23. 23.

    Chen, Z., Segev, M. & Christodoulides, D. N. Optical spatial solitons: historical overview and recent advances. Rep. Prog. Phys. 75, 086401 (2012).

    ADS  Article  Google Scholar 

  24. 24.

    Yang, J. & Musslimani, Z. H. Fundamental and vortex solitons in a two-dimensional optical lattice. Opt. Lett. 28, 2094–2096 (2003).

    ADS  Article  Google Scholar 

  25. 25.

    Efremidis, N. K. et al. Two-dimensional optical lattice solitons. Phys. Rev. Lett. 91, 213906 (2003).

    ADS  Article  Google Scholar 

  26. 26.

    Neshev, D., Ostrovskaya, E., Kivshar, Y. & Krolikowski, W. Spatial solitons in optically induced gratings. Opt. Lett. 28, 710–712 (2003).

    ADS  Article  Google Scholar 

  27. 27.

    Ablowitz, M. J., Ilan, B., Schonbrun, E. & Piestun, R. Solitons in two-dimensional lattices possessing defects, dislocations and quasicrystal structures. Phys. Rev. E 74, 035601 (2006) .

    ADS  MathSciNet  Article  Google Scholar 

  28. 28.

    Law, K. J. H., Saxena, A., Kevrekidis, P. G. & Bishop, A. R. Stable structures with high topological charge in nonlinear photonic quasicrystals. Phys. Rev. A 82, 035802 (2010).

    ADS  Article  Google Scholar 

  29. 29.

    Ablowitz, M. J., Antar, N., Bakirtas, I. & Ilan, B. Vortex and dipole solitons in complex two-dimensional nonlinear lattices. Phys. Rev. A 86, 033804 (2012).

    ADS  Article  Google Scholar 

  30. 30.

    Xavier, J., Boguslawski, M., Rose, P., Joseph, J. & Denz, C. Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures. Adv. Mater. 22, 356–360 (2010).

    Article  Google Scholar 

  31. 31.

    Chiao, R. Y., Garmire, E. & Townes, C. H. Self-trapping of optical beams. Phys. Rev. Lett. 13, 479 (1964).

    ADS  Article  Google Scholar 

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Q.F., P.W. and F.Y. acknowledge support from NSFC (grants 91950120 and 11690033) and the Natural Science Foundation of Shanghai (grant 19ZR1424400). P.W. and F.Y. thank X. Chen for support with experiments. Y.V.K. and L.T. acknowledge support from the Severo Ochoa Excellence Programme, Fundacio Privada Cellex, Fundacio Privada Mir-Puig and CERCA/Generalitat de Catalunya. V.V.K. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) under contract no. UIDB/00618/2020.

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All authors contributed significantly to the work.

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Correspondence to Fangwei Ye.

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Supplementary Information

Supplementary Figs. 1 and 2 and Discussion.

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Fu, Q., Wang, P., Huang, C. et al. Optical soliton formation controlled by angle twisting in photonic moiré lattices. Nat. Photonics 14, 663–668 (2020).

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