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.

  • Article
  • Published:

Three-dimensional nonlinear optical materials from twisted two-dimensional van der Waals interfaces

Abstract

To enable new nonlinear responses, metamaterials are created by organizing structural units (meta-atoms), which are typically on the scale of about a hundred nanometres. However, truly altering the atomic symmetry and enabling new nonlinear responses requires control at the atomic scale, down to a few ångströms. Here we report three-dimensional nonlinear optical materials realized by the precise control and twist of individual two-dimensional van der Waals interfaces. Specifically, new nonlinear crystals are achieved by adding pseudo-screw symmetries to a multiple of four-layer WS2 stacks (for example, four layer, eight layer and so on). Nonlinear susceptibility and circular selectivity of the resulting three-dimensional crystals are fundamentally different from natural WS2, demonstrating a microscopic analogue to the fabrication of metamaterials with unique optical properties. Furthermore, we show that the magnitude of the newly enabled nonlinearity is enhanced by controlling the number of interfaces and the excitation wavelength. Our findings suggest a new approach to redesign the intrinsic nonlinearity in artificial atomic configurations, scalable from a few-nanometre-thick unit cells to bulk materials.

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

Access options

Buy this article

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

Fig. 1: Redesigned second-order susceptibility in a twisted 3D crystal.
Fig. 2: Interfacial nonlinear susceptibility in twisted bilayer WS2.
Fig. 3: Scalability of interfacial nonlinear susceptibility in twisted trilayer WS2 stacks.
Fig. 4: Scalable nonlinear optical material.
Fig. 5: Enhanced nonlinear susceptibility by exciton resonances.
Fig. 6: Nonlinear circular selectivity enabled by a four-fold screw symmetry.

Similar content being viewed by others

Data availability

The data in the Article are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

  1. Boyd, R. W. Nonlinear Optics 3rd edn (Academic, 2008).

  2. Sutherland, R. L., McLean, D. G. & Kirkpatrick, S. Handbook of Nonlinear Optics 2nd edn (Marcel Dekker, 2003).

  3. Bergfeld, S. & Daum, W. Second-harmonic generation in GaAs: experiment versus theoretical predictions of \({\chi }_{xyz}^{(2)}\). Phys. Rev. Lett. 90, 036801 (2003).

    ADS  Google Scholar 

  4. Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).

    Google Scholar 

  5. Li, Y. et al. Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. Nano Lett. 13, 3329–3333 (2013).

    ADS  Google Scholar 

  6. Kauranen, M. & Zayats, A. V. Nonlinear plasmonics. Nat. Photon. 6, 737–748 (2012).

    ADS  Google Scholar 

  7. Lapine, M., Shadrivov, I. V. & Kivshar, Y. S. Colloquium: nonlinear metamaterials. Rev. Mod. Phys. 86, 1093–1123 (2014).

    ADS  Google Scholar 

  8. Li, G., Zhang, S. & Zentgraf, T. Nonlinear photonic metasurfaces. Nat. Rev. Mater. 2, 17010 (2017).

    ADS  Google Scholar 

  9. Kadic, M., Milton, G. W., van Hecke, M. & Wegener, M. 3D metamaterials. Nat. Rev. Phys. 1, 198–210 (2019).

    Google Scholar 

  10. Shen, Y. R. Surface properties probed by second-harmonic and sum-frequency generation. Nature 337, 519–525 (1989).

    ADS  Google Scholar 

  11. Guyot-Sionnest, P. & Shen, Y. R. Local and nonlocal surface nonlinearities for surface optical second-harmonic generation. Phys. Rev. B 35, 4420–4426 (1987).

    ADS  Google Scholar 

  12. Cazzanelli, M. & Schilling, J. Second order optical nonlinearity in silicon by symmetry breaking. Appl. Phys. Rev. 3, 011104 (2016).

    ADS  Google Scholar 

  13. Lee, J. et al. Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions. Nature 511, 65–69 (2014).

    ADS  Google Scholar 

  14. Butet, J., Brevet, P.-F. & Martin, O. J. F. Optical second harmonic generation in plasmonic nanostructures: from fundamental principles to advanced applications. ACS Nano 9, 10545–10562 (2015).

    Google Scholar 

  15. Linnenbank, H., Grynko, Y., Förstner, J. & Linden, S. Second harmonic generation spectroscopy on hybrid plasmonic/dielectric nanoantennas. Light: Sci. Appl. 5, e16013 (2016).

    ADS  Google Scholar 

  16. Khurgin, J. B. How to deal with the loss in plasmonics and metamaterials. Nat. Nanotechnol. 10, 2–6 (2015).

    ADS  Google Scholar 

  17. Bonacina, L., Brevet, P.-F., Finazzi, M. & Celebrano, M. Harmonic generation at the nanoscale. J. Appl. Phys. 127, 230901 (2020).

    ADS  Google Scholar 

  18. Valev, V. K. Characterization of nanostructured plasmonic surfaces with second harmonic generation. Langmuir 28, 15454–15471 (2012).

    Google Scholar 

  19. Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).

    ADS  Google Scholar 

  20. Angeli, M. & MacDonald, A. H. Γ valley transition metal dichalcogenide moiré bands. Proc. Natl Acad. Sci. USA 118, e2021826118 (2021).

    Google Scholar 

  21. Zhang, Y., Liu, T. & Fu, L. Electronic structures, charge transfer, and charge order in twisted transition metal dichalcogenide bilayers. Phys. Rev. B 103, 155142 (2021).

    ADS  Google Scholar 

  22. Zhou, B. T., Egan, S. & Franz, M. Moiré flat Chern bands and correlated quantum anomalous Hall states generated by spin-orbit couplings in twisted homobilayer MoS2. Phys. Rev. Res. 4, L012032 (2022).

    Google Scholar 

  23. Yang, F. et al. Tunable second harmonic generation in twisted bilayer graphene. Matter 3, 1361–1376 (2020).

    Google Scholar 

  24. Hsu, W.-T. et al. Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers. ACS Nano 8, 2951–2958 (2014).

    Google Scholar 

  25. Paradisanos, I. et al. Second harmonic generation control in twisted bilayers of transition metal dichalcogenides. Phys. Rev. B 105, 115420 (2022).

    ADS  Google Scholar 

  26. van der Zande, A. M. et al. Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14, 3869–3875 (2014).

    ADS  Google Scholar 

  27. Liu, K. et al. Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5, 4966 (2014).

    ADS  Google Scholar 

  28. Yao, K. et al. Enhanced tunable second harmonic generation from twistable interfaces and vertical superlattices in boron nitride homostructures. Sci. Adv. 7, eabe8691 (2021).

    ADS  Google Scholar 

  29. Koshelev, K. et al. Subwavelength dielectric resonators for nonlinear nanophotonics. Science 367, 288–292 (2020).

    ADS  Google Scholar 

  30. Anthur, A. P. et al. Continuous wave second harmonic generation enabled by quasi-bound-states in the continuum on gallium phosphide metasurfaces. Nano Lett. 20, 8745–8751 (2020).

    ADS  Google Scholar 

  31. Ray, P. C. Size and shape dependent second order nonlinear optical properties of nanomaterials and their application in biological and chemical sensing. Chem. Rev. 110, 5332–5365 (2010).

    Google Scholar 

  32. Deka, G., Sun, C.-K., Fujita, K. & Chu, S.-W. Nonlinear plasmonic imaging techniques and their biological applications. Nanophotonics 6, 31–49 (2017).

    Google Scholar 

  33. Hickstein, D. D. et al. Self-organized nonlinear gratings for ultrafast nanophotonics. Nat. Photon. 13, 494–499 (2019).

    ADS  Google Scholar 

  34. Yu, W. et al. High-yield exfoliation of monolayer 1T’-MoTe2 as saturable absorber for ultrafast photonics. ACS Nano 15, 18448–18457 (2021).

    Google Scholar 

  35. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    ADS  Google Scholar 

  36. Javerzac-Galy, C. et al. On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator. Phys. Rev. A 94, 053815 (2016).

    ADS  Google Scholar 

  37. Fan, L. et al. Superconducting cavity electro-optics: a platform for coherent photon conversion between superconducting and photonic circuits. Sci. Adv. 4, eaar4994 (2018).

    ADS  Google Scholar 

  38. Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  40. Liu, F. et al. Disassembling 2D van der Waals crystals into macroscopic monolayers and reassembling into artificial lattices. Science 367, 903–906 (2020).

    ADS  Google Scholar 

  41. Okada, M., Takizawa, K. & Ieiri, S. The measurement of the antisymmetric components of nonlinear optical susceptibilities of TeO2 crystal. J. Appl. Phys. 48, 4163–4167 (1977).

    ADS  Google Scholar 

  42. Zhao, H.-J., Zhang, Y.-F. & Chen, L. Strong Kleinman-forbidden second harmonic generation in chiral sulfide: La4InSbS9. J. Am. Chem. Soc. 134, 1993–1995 (2012).

    Google Scholar 

  43. Husu, H. et al. Metamaterials with tailored nonlinear optical response. Nano Lett. 12, 673–677 (2012).

    ADS  Google Scholar 

  44. Czaplicki, R. et al. Enhancement of second-harmonic generation from metal nanoparticles by passive elements. Phys. Rev. Lett. 110, 093902 (2013).

    ADS  Google Scholar 

  45. Byers, J. D., Yee, H. I., Petralli-Mallow, T. & Hicks, J. M. Second-harmonic generation circular-dichroism spectroscopy from chiral monolayers. Phys. Rev. B 49, 14643–14647 (1994).

    ADS  Google Scholar 

  46. Belardini, A. et al. Circular dichroism in the optical second-harmonic emission of curved gold metal nanowires. Phys. Rev. Lett. 107, 257401 (2011).

    ADS  Google Scholar 

  47. Ghosh, A. & Fischer, P. Chiral molecules split light: reflection and refraction in a chiral liquid. Phys. Rev. Lett. 97, 173002 (2006).

    ADS  Google Scholar 

  48. Fan, X. et al. Mechanism of extreme optical nonlinearities in spiral WS2 above the bandgap. Nano Lett. 20, 2667–2673 (2020).

    ADS  Google Scholar 

  49. Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).

    ADS  Google Scholar 

  50. Chen, S. et al. Symmetry-selective third-harmonic generation from plasmonic metacrystals. Phys. Rev. Lett. 113, 033901 (2014).

    ADS  Google Scholar 

  51. Zhang, C., Li, Z.-Q., Yang, X., Chen, Z. & Wang, Z. Controlling third harmonic generation with gammadion-shaped chiral metamaterials. AIP Adv. 6, 125014 (2016).

    ADS  Google Scholar 

  52. Saito, N. et al. Observation of selection rules for circularly polarized fields in high-harmonic generation from a crystalline solid. Optica 4, 1333–1336 (2017).

    ADS  Google Scholar 

  53. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    ADS  Google Scholar 

  54. Kazmierczak, N. P. et al. Strain fields in twisted bilayer graphene. Nat. Mater. 20, 956–963 (2021).

    ADS  Google Scholar 

  55. Ci, P. et al. Breaking rotational symmetry in supertwisted WS2 spirals via moiré magnification of intrinsic heterostrain. Nano Lett. 22, 9027–9035 (2022).

    ADS  Google Scholar 

  56. Sun, L. et al. Separation of valley excitons in a MoS2 monolayer using a subwavelength asymmetric groove array. Nat. Photon. 13, 180–184 (2019).

    ADS  Google Scholar 

  57. Shreiner, R., Hao, K., Butcher, A. & High, A. A. Electrically controllable chirality in a nanophotonic interface with a two-dimensional semiconductor. Nat. Photon. 16, 330–336 (2022).

    ADS  Google Scholar 

  58. Lodahl, P. et al. Chiral quantum optics. Nature 541, 473–480 (2017).

    ADS  Google Scholar 

  59. Zhang, Y. et al. Chirality logic gates. Sci. Adv. 8, eabq8246 (2022).

    ADS  Google Scholar 

  60. Hu, G. et al. Coherent steering of nonlinear chiral valley photons with a synthetic Au-WS2 metasurface. Nat. Photon. 13, 467–472 (2019).

    ADS  Google Scholar 

  61. Newnham, R. E. Properties of Materials: Anisotropy, Symmetry, Structure (Oxford Univ. Press, 2004).

  62. Hu, C., Wang, R. & Ding, D.-H. Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Progr. Phys. 63, 1–39 (2000).

    MathSciNet  ADS  Google Scholar 

  63. Duerloo, K.-A. N., Ong, M. T. & Reed, E. J. Intrinsic piezoelectricity in two-dimensional materials. J. Phys. Chem. Lett. 3, 2871–2876 (2012).

    Google Scholar 

  64. Hu, L. et al. Localized symmetry breaking for tuning thermal expansion in ScF3 nanoscale frameworks. J. Am. Chem. Soc. 140, 4477–4480 (2018).

    Google Scholar 

Download references

Acknowledgements

This work was partly supported by the National Science Foundation through the University of Pennsylvania Materials Research Science and Engineering Center DMR-1720530 (B.K.), the US Office of Naval Research (ONR) through grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection (B.Z., B.K., J.J., Z.W., L.H. and T.C.) and grant N00014-21-1-2703 (B.Z., B.K., J.J., Z.W., L.H. and T.C.) and the Sloan Foundation (B.Z.). Work by E.J.M. is supported by the Department of Energy under grant DE-FG02-84ER45118. T.C. acknowledges the support of a research grant (project no. 42106) from Villum Fonden.

Author information

Authors and Affiliations

Authors

Contributions

B.Z. and B.K. conceived the project. B.K. and Z.W. fabricated the twisted stacks. B.K. performed the SHG measurements assisted by J.J. and L.H. B.K. and T.C. performed the symmetry analysis. B.Z., E.J.M. and B.K. discussed and interpreted the results. B.Z. and B.K. wrote the paper with input from all authors. All authors discussed the results.

Corresponding author

Correspondence to Bo Zhen.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Wen-Hao Chang and the other, anonymous, reviewer(s) 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.

Supplementary information

Supplementary Information

Supplementary Sections I–X, Figs. 1–8, Equations (1)–(30) and Tables 1–3.

Reporting Summary

Source data

Source Data Fig. 2

Statistical source data for Fig. 2.

Source Data Fig. 3

Statistical source data for Fig. 3.

Source Data Fig. 4

Statistical source data for Fig. 4.

Source Data Fig. 5

Statistical source data for Fig. 5.

Source Data Fig. 6

Statistical source data for Fig. 6.

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

Kim, B., Jin, J., Wang, Z. et al. Three-dimensional nonlinear optical materials from twisted two-dimensional van der Waals interfaces. Nat. Photon. 18, 91–98 (2024). https://doi.org/10.1038/s41566-023-01318-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-023-01318-6

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