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:

Tunable self-assembled Casimir microcavities and polaritons

Nature volume 597, pages 214–219 (2021)Cite this article

Subjects

Abstract

Spontaneous formation of ordered structures—self-assembly—is ubiquitous in nature and observed on different length scales, ranging from atomic and molecular systems to micrometre-scale objects and living matter1. Self-ordering in molecular and biological systems typically involves short-range hydrophobic and van der Waals interactions2,3. Here we introduce an approach to micrometre-scale self-assembly based on the joint action of attractive Casimir and repulsive electrostatic forces arising between charged metallic nanoflakes in an aqueous solution. This system forms a self-assembled optical Fabry–Pérot microcavity with a fundamental mode in the visible range (long-range separation distance about 100–200 nanometres) and a tunable equilibrium configuration. Furthermore, by placing an excitonic material in the microcavity region, we are able to realize hybrid light–matter states (polaritons4,5,6), whose properties, such as coupling strength and eigenstate composition, can be controlled in real time by the concentration of ligand molecules in the solution and light pressure. These Casimir microcavities could find future use as sensitive and tunable platforms for a variety of applications, including opto-mechanics7, nanomachinery8 and cavity-induced polaritonic chemistry9.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: The self-assembled microcavity system and the physical mechanism behind its operation.
Fig. 2: Self-assembled trimer cavities.
Fig. 3: Self-assembled cavities in nanoflake-on-static-mirror configuration and the formation of polaritons.
Fig. 4: Actively tunable microcavities and polaritons.

Similar content being viewed by others

Data availability

The set of experimental and calculated optical spectra, SEM images, optical images and numerical codes are available through figshare.com with the identifier https://doi.org/10.6084/m9.figshare.14883024.v2. Additional data are available from T.O.S. upon request.

References

  1. Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).

    Article  CAS  ADS  Google Scholar 

  2. Min, Y., Akbulut, M., Kristiansen, K., Golan, Y. & Israelachvili, J. in Nanoscience and Technology: a Collection of Reviews from Nature Journals (ed. Rodgers, P.) 38–49 (World Scientific/Nature Publishing Group, 2010).

  3. Batista, C. A. S., Larson, R. G. & Kotov, N. A. Nonadditivity of nanoparticle interactions. Science 350, 1242477 (2015).

    Article  Google Scholar 

  4. Khitrova, G., Gibbs, H., Kira, M., Koch, S. W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nat. Phys. 2, 81–90 (2006).

    Article  CAS  Google Scholar 

  5. Törmä, P. & Barnes, W. L. Strong coupling between surface plasmon polaritons and emitters: a review. Rep. Prog. Phys. 78, 013901 (2015).

    Article  ADS  Google Scholar 

  6. Baranov, D. G., Wersäll, M., Cuadra, J., Antosiewicz, T. J. & Shegai, T. Novel nanostructures and materials for strong light-matter interactions. ACS Photon. 5, 24–42 (2018).

    Article  CAS  Google Scholar 

  7. Eichenfield, M., Camacho, R., Chan, J., Vahala, K. J. & Painter, O. A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature 459, 550–555 (2009).

    Article  CAS  ADS  Google Scholar 

  8. Zhao, R. et al. Stable Casimir equilibria and quantum trapping. Science 364, 984–987 (2019).

    Article  CAS  ADS  Google Scholar 

  9. Thomas, A. et al. Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field. Angew. Chem. Int. Edn 55, 11462–11466 (2016).

    Article  CAS  Google Scholar 

  10. Casimir, H. B. G. On the attraction between two perfectly conducting plates. Kon. Ned. Akad. Wetensch. Proc. 51, 793–795 (1948).

    MATH  Google Scholar 

  11. Rodriguez, A. W. et al. Classical and fluctuation-induced electromagnetic interactions in micron-scale systems: designer bonding, antibonding, and Casimir forces. Ann. Phys. 527, 45–80 (2015).

    Article  Google Scholar 

  12. Derjaguin, B. V. & Landau, L. D. Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. URSS 14, 633–662 (1941).

    Google Scholar 

  13. Verwey, E. J. W. Theory of the stability of lyophobic colloids. J. Phys. Chem. 51, 631–636 (1947).

    Article  CAS  Google Scholar 

  14. Lifshitz, E. M. The theory of molecular attractive forces between solids. Sov. Phys. JETP 2, 73–83 (1956).

    Google Scholar 

  15. Dzyaloshinskii, I. E., Lifshitz, E. M. & Pitaevskii, L. P. The general theory of van der Waals forces. Adv. Phys. 10, 165–209 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  16. van Blokland, P. H. & Overbeek, J. T. G. Van der Waals forces between objects covered with a chromium layer. J. Chem. Soc. Faraday Trans. I 74, 2637–2651 (1978).

    Article  Google Scholar 

  17. Lamoreaux, S. K. Demonstration of the Casimir force in the 0.6 to 6 μm range. Phys. Rev. Lett. 78, 5–8 (1997).

    Article  CAS  ADS  Google Scholar 

  18. Bressi, G., Carugno, G., Onofrio, R. & Ruoso, G. Measurement of the Casimir force between parallel metallic surfaces. Phys. Rev. Lett. 88, 041804 (2002).

    Article  CAS  ADS  Google Scholar 

  19. Munday, J. N., Capasso, F. & Parsegian, V. A. Measured long-range repulsive Casimir–Lifshitz forces. Nature 457, 170–173 (2009).

    Article  CAS  ADS  Google Scholar 

  20. Munday, J. & Capasso, F. Repulsive Casimir and van der Waals forces: from measurements to future technologies. Int. J. Mod. Phys. A 25, 2252–2259 (2010).

    Article  CAS  ADS  Google Scholar 

  21. Tang, L. et al. Measurement of non-monotonic Casimir forces between silicon nanostructures. Nat. Photon. 11, 97–101 (2017).

    Article  CAS  ADS  Google Scholar 

  22. Cho, Y. K., Wartena, R., Tobias, S. M. & Chiang, Y.-M. Self-assembling colloidal-scale devices: selecting and using short-range surface forces between conductive solids. Adv. Funct. Mater. 17, 379–389 (2007).

    Article  CAS  Google Scholar 

  23. Biggs, S. & Mulvaney, P. Measurement of the forces between gold surfaces in water by atomic force microscopy. J. Chem. Phys. 100, 8501–8505 (1994).

    Article  CAS  ADS  Google Scholar 

  24. Israelachvili, J. N. Intermolecular and Surface Forces (Academic, 2015).

  25. Chen, S. et al. Rapid seedless synthesis of gold nanoplates with microscaled edge length in a high yield and their application in SERS. Nano-Micro Lett. 8, 328–335 (2016).

    Article  Google Scholar 

  26. Li, R. et al. Study on the assembly structure variation of cetyltrimethylammonium bromide on the surface of gold nanoparticles. ACS Omega 5, 4943–4952 (2020).

    Article  CAS  Google Scholar 

  27. Liu, Y., Tourbin, M., Lachaize, S. & Guiraud, P. Silica nanoparticles separation from water: aggregation by cetyltrimethylammonium bromide (CTAB). Chemosphere 92, 681–687 (2013).

    Article  CAS  ADS  Google Scholar 

  28. Chen, F., Mohideen, U., Klimchitskaya, G. & Mostepanenko, V. Demonstration of the lateral Casimir force. Phys. Rev. Lett. 88, 101801 (2002).

    Article  CAS  ADS  Google Scholar 

  29. Chen, F., Mohideen, U., Klimchitskaya, G. & Mostepanenko, V. Experimental and theoretical investigation of the lateral Casimir force between corrugated surfaces. Phys. Rev. A 66, 032113 (2002).

    Article  ADS  Google Scholar 

  30. Rodrigues, R. B., Neto, P. A. M., Lambrecht, A. & Reynaud, S. Lateral Casimir force beyond the proximity-force approximation. Phys. Rev. Lett. 96, 100402 (2006).

    Article  ADS  Google Scholar 

  31. Meyer, M., Le Ru, E. & Etchegoin, P. Self-limiting aggregation leads to long-lived metastable clusters in colloidal solutions. J. Phys. Chem. B 110, 6040–6047 (2006).

    Article  CAS  Google Scholar 

  32. Junginger, A. et al. Tunable strong coupling of two adjacent optical λ/2 Fabry-Pérot microresonators. Opt. Express 28, 485–493 (2020).

    Article  CAS  ADS  Google Scholar 

  33. Berkhout, A., Wolterink, T. A. & Koenderink, A. F. Strong coupling to generate complex birefringence: metasurface in the middle etalons. ACS Photon. 7, 2799 (2020).

    Article  CAS  Google Scholar 

  34. Li, Y. et al. Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2. Phys. Rev. B 90, 205422 (2014).

    Article  ADS  Google Scholar 

  35. Gatemala, H., Pienpinijtham, P., Thammacharoen, C. & Ekgasit, S. Rapid fabrication of silver microplates under an oxidative etching environment consisting of O2/Cl−, NH4OH/H2O2, and H2O2. CrystEngComm 17, 5530–5537 (2015).

    Article  CAS  Google Scholar 

  36. 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 

  37. Shegai, T., Brian, B., Miljkovic, V. D. & Käll, M. Angular distribution of surface-enhanced Raman scattering from individual au nanoparticle aggregates. ACS Nano 5, 2036–2041 (2011).

    Article  CAS  Google Scholar 

  38. Lifshitz, E. M. et al. in Perspectives in Theoretical Physics (ed. Pitaevski, L. P.) 329–349 (Elsevier, 1992).

  39. Johnson, P. B. & Christy, R.-W. Optical constants of the noble metals. Phys. Rev. B 6, 4370 (1972).

    Article  CAS  ADS  Google Scholar 

  40. Segelstein, D. The Complex Refractive Index of Water. MSc thesis, Univ. Missouri (1981).

  41. Kadirov, M. K., Litvinov, A. I., Nizameev, I. R. & Zakharova, L. Y. Adsorption and premicellar aggregation of CTAB molecules and fabrication of nanosized platinum lattice on the glass surface. J. Phys. Chem. C 118, 19785–19794 (2014).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge K. Eliasson for help with Raman measurements, as well as E. Tornéus, A. B. Yankovich, P. Erhart and M. Käll for stimulating discussions. The authors acknowledge financial support from the Swedish Research Council (under the VR Miljö project, grant no. 2016-06059 to T.O.S; and the VR project, grant no. 2017-04545 to T.O.S), the Knut and Alice Wallenberg Foundation (project no. 2019.0140 to T.O.S.), and the Chalmers Excellence Initiative Nano.

Author information

Authors and Affiliations

  1. Department of Physics, Chalmers University of Technology, Gothenburg, Sweden

    Battulga Munkhbat, Adriana Canales, Betül Küçüköz, Denis G. Baranov & Timur O. Shegai

  2. Center for Photonics and 2D Materials, Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Denis G. Baranov

Authors
  1. Battulga Munkhbat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adriana Canales
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Betül Küçüköz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Denis G. Baranov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Timur O. Shegai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.M. and T.O.S. conceived the idea. B.M. fabricated the samples. B.M. and A.C. performed optical measurements. B.M. and B.K. investigated active tuning of the structures. D.G.B. performed theoretical analysis of the experimental data. B.M., D.G.B. and T.O.S. wrote the manuscript with input from all co-authors. T.O.S. supervised the study.

Corresponding author

Correspondence to Timur O. Shegai.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Jeremy Munday and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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

Supplementary information

Supplementary Information

This file contains Supplementary Notes 1 – 5, Supplementary Text, Supplementary Figures 1 – 25, Supplementary Tables 1 – 3, legends for Supplementary Videos 1 – 6 and Supplementary References.

Supplementary Video 1

A stable gold nanoflake dimer as well as formation of a dimer.

Supplementary Video 2

Relative displacement of top and bottom nanoflakes within a self-assembled dimer along x and y directions as a function of time. Note that while flakes can move and rotate with respect to each other, their relative displacement is always small in comparison to the lateral size of the flakes. This indicated the dimer stability not only in vertical, but also in lateral directions.

Supplementary Video 3

A stable gold nanoflake trimer.

Supplementary Video 4

Relative displacement of top, middle, and bottom nanoflakes within a trimer along x and y directions as a function of time. This video shows that the self-assembled trimer exhibits an equilibrium not only in vertical direction, but also in lateral directions.

Supplementary Video 5

Additional examples of stable self-assembled multi-stacks of gold nanoflakes.

Supplementary Video 6

Additional examples of stable self-assembled multi-stacks of gold nanoflakes.

Peer Review File

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Munkhbat, B., Canales, A., Küçüköz, B. et al. Tunable self-assembled Casimir microcavities and polaritons. Nature 597, 214–219 (2021). https://doi.org/10.1038/s41586-021-03826-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-03826-3

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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