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.

Photonic topological Anderson insulators

Abstract

The hallmark property of two-dimensional topological insulators is robustness of quantized electronic transport of charge and energy against disorder in the underlying lattice1. That robustness arises from the fact that, in the topological bandgap, such transport can occur only along the edge states, which are immune to backscattering owing to topological protection. However, for sufficiently strong disorder, this bandgap closes and the system as a whole becomes topologically trivial: all states are localized and all transport vanishes in accordance with Anderson localization2,3. The recent suggestion4 that the reverse transition can occur was therefore surprising. In so-called topological Anderson insulators, it has been predicted4 that the emergence of protected edge states and quantized transport can be induced, rather than inhibited, by the addition of sufficient disorder to a topologically trivial insulator. Here we report the experimental demonstration of a photonic topological Anderson insulator. Our experiments are carried out in an array of helical evanescently coupled waveguides in a honeycomb geometry with detuned sublattices. Adding on-site disorder in the form of random variations in the refractive index of the waveguides drives the system from a trivial phase into a topological one. This manifestation of topological Anderson insulator physics shows experimentally that disorder can enhance transport rather than arrest it.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Floquet topological Anderson insulator in a detuned honeycomb lattice.
Fig. 2: Set-up and functionality of the lattice system.
Fig. 3: Engineering the topologically trivial phase.
Fig. 4: Formation of the photonic topological Anderson insulator.

References

  1. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  CAS  Google Scholar 

  2. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  4. Li, J., Chu, R.-L., Jain, J. K. & Shen, S.-Q. Topological Anderson insulator. Phys. Rev. Lett. 102, 136806 (2009).

    Article  ADS  PubMed  CAS  Google Scholar 

  5. Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

    Article  ADS  PubMed  CAS  Google Scholar 

  6. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

    Article  ADS  CAS  Google Scholar 

  7. Cheng, X. et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater. 15, 542–548 (2016).

    Article  ADS  PubMed  CAS  Google Scholar 

  8. Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

    Article  ADS  PubMed  CAS  Google Scholar 

  9. Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljacic, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

    Article  ADS  PubMed  CAS  Google Scholar 

  10. Umucalılar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

    Article  ADS  CAS  Google Scholar 

  11. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

    Article  CAS  Google Scholar 

  12. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).

    Article  ADS  CAS  Google Scholar 

  13. Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013).

    Article  ADS  PubMed  CAS  Google Scholar 

  14. Maczewsky, L. J., Zeuner, J. M., Nolte, S. & Szameit, A. Observation of photonic anomalous Floquet topological insulators. Nat. Commun. 8, 13756 (2017).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  15. Mukherjee, S. et al. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice. Nat. Commun. 8, 13918 (2017).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  16. Khanikaev, A. B., Fleury, R., Mousavi, S. H. & Alù, A. Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6, 8260 (2015).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  17. Yang, Z. et al. Topological acoustics. Phys. Rev. Lett. 114, 114301 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  18. Süsstrunk, R. & Huber, S. D. Observation of phononic helical edge states in a mechanical topological insulator. Science 349, 47–50 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  19. Nash, L. M. et al. Topological mechanics of gyroscopic metamaterials. Proc. Natl Acad. Sci. USA 112, 14495–14500 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  20. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  21. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2014).

    Article  CAS  Google Scholar 

  22. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  ADS  PubMed  CAS  Google Scholar 

  23. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

    Article  ADS  PubMed  CAS  Google Scholar 

  24. Rechtsman, M. C. et al. Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013).

    Article  ADS  CAS  Google Scholar 

  25. Weimann, S. et al. Topologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater. 16, 433–438 (2017).

    Article  ADS  PubMed  CAS  Google Scholar 

  26. Plotnik, Y. et al. Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107, 183901 (2011).

    Article  ADS  PubMed  CAS  Google Scholar 

  27. Titum, P., Lindner, N. H., Rechtsman, M. C. & Refael, G. Disorder-induced Floquet topological insulators. Phys. Rev. Lett. 114, 056801 (2015).

    Article  ADS  PubMed  CAS  Google Scholar 

  28. Guo, H.-M., Rosenberg, G., Refael, G. & Franz, M. Topological Anderson insulator in three dimensions. Phys. Rev. Lett. 105, 216601 (2010).

  29. Szameit, A. & Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B 43, 163001 (2010).

    Article  ADS  CAS  Google Scholar 

  30. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).

    Article  CAS  Google Scholar 

  31. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  ADS  CAS  Google Scholar 

  32. Rudner, M. S., Lindner, N. H., Berg, E. & Levin, M. Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems. Phys. Rev. X 3, 031005 (2013).

    CAS  Google Scholar 

  33. Titum, P., Berg, E., Rudner, M. S., Refael, G. & Lindner, N. H. Anomalous Floquet-Anderson insulator as a nonadiabatic quantized charge pump. Phys. Rev. X 6, 021013 (2016).

    Google Scholar 

  34. Meier, E. J. et al. Observation of the topological Anderson insulator in disordered atomic wires. Preprint at https://arxiv.org/abs/1802.02109 (2018).

  35. Groth, C. W. et al. Theory of the topological Anderson insulator. Phys. Rev. Lett. 103, 196805 (2019).

    Article  ADS  Google Scholar 

  36. Titum, P., Lindner, N. H. & Refael, G. Disorder-induced transitions in resonantly driven Floquet topological insulators. Phys. Rev. B 96, 054207 (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

A.S. and M.S. thank the German-Israeli DIP (project BL 574/13-1). A.S. acknowledges funding from the German Research Foundation (project SZ 276/9-1). M.S. thanks the European Research Council for financial support. N.L. acknowledges financial support from the European Research Council under the European Union Horizon 2020 Research and Innovation Programme (grant agreement number 639172), from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 631696 and from the Israeli Center of Research Excellence (I-CORE) Circle of Light, funded by the Israeli Science Foundation. M.C.R. acknowledges support from the National Science Foundation under grant number DMS-1620422, as well as the Sloan (FG-2016-6418) and Kaufman (KA2017-91788) foundations. P.T. is supported by an NRC postdoctoral fellowship. The authors acknowledge the University of Maryland supercomputing resources made available for conducting the research reported in this paper.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed substantially to this work.

Corresponding author

Correspondence to Alexander Szameit.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Extended data figures and tables

Extended Data Fig. 1 Experimental and numerical results for the disordered system.

a, The averaged intensity profile of the edge state, which peaks at the waveguide positions. b, A fit through the waveguide peak intensities decays exponentially, with a decay length of 47 μm. c, The function gN(r0rε), integrated along the edge, showing a decay length of about 7a. The inset shows the simulated displacement of the wavefunction along the edge for the parameters listed in Methods, from which the group velocity can be extracted. d, The function gN(r0rε), for an initial position r0 deep in the bulk of the system, showing that the bulk localization length is approximately 4a.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Stützer, S., Plotnik, Y., Lumer, Y. et al. Photonic topological Anderson insulators. Nature 560, 461–465 (2018). https://doi.org/10.1038/s41586-018-0418-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-018-0418-2

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

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