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Topological states in photonic systems

Nature Physics volume 12, pages 626–629 (2016)Cite this article

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Optics played a key role in the discovery of geometric phase. It now joins the journey of exploring topological physics, bringing bosonic topological states that equip us with the ability to make perfect photonic devices using imperfect interfaces.

In 1956, a 22-year-old Indian physicist known as Pancharatnam1 showed that, over the course of a cyclic evolution, the polarization vector of light acquires a phase that is only determined by the area of the cycle on the Poincaré sphere. Three years later, the celebrated Aharonov–Bohm phase was discovered2. After more than two decades, Berry3 generalized these two geometric phases into what we now call the 'Berry phases', which were subsequently demonstrated experimentally in coiled optical fibres4. It was immediately realized5 that the Berry phase is closely connected with the topological interpretation6 of the integer quantum Hall effect (QHE), which was discovered in 1980. In particular, the signed integers (Z) in the quantized edge conductance are mathematically equivalent to the bulk Chern numbers of the fibre bundle theory in topology (see Commentary by Asorey7). Another example of the bulk-edge correspondence was shown by Zak8, who demonstrated that the bulk Berry phase differentiates the Tamm and Shockley states9, found in the 1930s, at the ends of one-dimensional (1D) lattices.

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Figure 1: One-way dispersions and circuit.
Figure 2: Weyl points in a gyroid photonic crystal.
Figure 3: A single-Dirac-cone surface state immune to random disorder.

References

  1. Pancharatnam, S. Proc. Indiana Acad. Sci. A 44, 247–262 (1956).

    Article  MathSciNet  Google Scholar 

  2. Aharonov, Y. & Bohm, D. Phys. Rev. 115, 485–491 (1959).

    Article  ADS  MathSciNet  Google Scholar 

  3. Berry, M.V. Proc. R. Soc. A 392, 45–57 (1984).

    Article  ADS  Google Scholar 

  4. Tomita, A. & Chiao, R. Y. Phys. Rev. Lett. 57, 937–940 (1986).

    Article  ADS  Google Scholar 

  5. Simon, B. Phys. Rev. Lett. 51, 2167–2170 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  6. Thouless, D.J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Phys. Rev. Lett. 49, 405–408 (1982).

    Article  ADS  Google Scholar 

  7. Asorey, M. Nature Phys. 12, 616–618 (2016).

    Article  ADS  Google Scholar 

  8. Zak, J. Phys. Rev. Lett. 62, 2747–2750 (1989).

    Article  ADS  Google Scholar 

  9. Shockley, W. Phys. Rev. 56, 317–323 (1939).

    Article  ADS  Google Scholar 

  10. Haldane, F. D. M. Phys. Rev. Lett. 61, 2015–2018 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  11. Kane, C. L. & Mele, E. J. Phys. Rev. Lett. 95, 226801 (2005).

    Article  ADS  Google Scholar 

  12. Lu, L., Joannopoulos, J. D. & Soljačić, M. Nature Photon. 8, 821–829 (2014).

    Article  ADS  Google Scholar 

  13. Kraus, Y. E. & Zilberberg, O. Nature Phys. 12, 624–626 (2016).

    Article  ADS  Google Scholar 

  14. Beenakker, C. & Kouwenhoven, L. Nature Phys. 12, 618–621 (2016).

    Article  ADS  Google Scholar 

  15. Huber, S. D. Nature Phys. 12, 621–623 (2016).

    Article  ADS  Google Scholar 

  16. Jin, D. et al. Preprint at http://arxiv.org/abs/1602.00553 (2016).

  17. Haldane, F. D. M. & Raghu, S. Phys. Rev. Lett. 100, 013904 (2008).

    Article  ADS  Google Scholar 

  18. Raghu, S. & Haldane, F. D. M. Phys. Rev. A 78, 033834 (2008).

    Article  ADS  Google Scholar 

  19. Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Soljačić, M. Phys. Rev. Lett. 100, 013905 (2008).

    Article  ADS  Google Scholar 

  20. Wang, Z., Chong, Y. D., Joannopoulos, J. D. & Soljačić, M. Nature 461, 772–775 (2009).

    Article  ADS  Google Scholar 

  21. Skirlo, S., Lu, L. & Soljačić, M. Phys. Rev. Lett. 113, 113904 (2014).

    Article  ADS  Google Scholar 

  22. Skirlo, S. A. et al. Phys. Rev. Lett. 115, 253901 (2015).

    Article  ADS  Google Scholar 

  23. Fang, K., Yu, Z. & Fan, S. Nature Photon. 6, 782–787 (2012).

    Article  ADS  Google Scholar 

  24. Rechtsman, M. C. et al. Nature 496, 196–200 (2013).

    Article  ADS  Google Scholar 

  25. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Nature Phys. 7, 907–912 (2011).

    Article  ADS  Google Scholar 

  26. Liang, G. Q. & Chong, Y. D. Phys. Rev. Lett. 110, 203904 (2013).

    Article  ADS  Google Scholar 

  27. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Nature Photon. 7, 1001–1005 (2013).

    Article  ADS  Google Scholar 

  28. Gao, F. et al. Nature Commun. 7, 11619 (2016).

    Article  ADS  Google Scholar 

  29. Khanikaev, A. B. et al. Nature Mater. 12, 233–239 (2013).

    Article  ADS  Google Scholar 

  30. Chen, W. et al. Nature Commun. 5, 5782 (2014).

    Article  ADS  Google Scholar 

  31. Cheng, X. Nature Mater. 15, 542–548 (2016).

    Article  ADS  Google Scholar 

  32. Wu, L. H. & Hu, X. Phys. Rev. Lett. 114, 223901 (2015).

    Article  ADS  Google Scholar 

  33. Lu, L., Fu, L., Joannopoulos, J. D. & Soljačić, M. Nature Photon. 7, 294–299 (2013).

    Article  ADS  Google Scholar 

  34. Fang, C., Lu, L., Liu, J. & Fu, L. Nature Phys. http://dx.doi.org/10.1038/nphys3782 (2016).

  35. Lu, L. et al. Science 349, 622–624 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  36. Gao, W. et al. Preprint at http://arxiv.org/abs/1511.04875 (2015).

  37. Silveirinha, M. G. Phys. Rev. B 92, 125153 (2015).

    Article  ADS  Google Scholar 

  38. Lu, L. et al. Nature Phys. 12, 337–340 (2016).

    Article  ADS  Google Scholar 

  39. Yang, Y. et al. Appl. Phys. Lett. 102, 231113 (2013).

    Article  ADS  Google Scholar 

  40. Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Phys. Rev. Lett. 113, 257401 (2014).

    Article  ADS  Google Scholar 

  41. Zeuner, J. M. et al. Phys. Rev. Lett. 115, 040402 (2015).

    Article  ADS  Google Scholar 

  42. Goldman, N., Budich, J. C. & Zoller, P. Nature Phys. 12, 639–645 (2016).

    Article  ADS  Google Scholar 

  43. Umucalılar, R. O. & Carusotto, I. Phys. Rev. Lett. 108, 206809 (2012).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank P. Rebusco for critical reading and editing of the manuscript. J.D.J. was supported in part by the US Army Research Office through the Institute for Soldier Nanotechnologies under contract W911NF-13-D-0001. L.L. was supported in part by the Materials Research Science and Engineering Center Program of the NSF under award DMR-1419807. M.S. and L.L. (analysis and reading of the manuscript) were supported in part by the MIT Solid-State Solar-Thermal Energy Conversion Center and Energy Frontier Research Center of DOE under grant DE-SC0001299. L.L. is also supported by the National Thousand-Young-Talents Program of China.

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Authors and Affiliations

  1. Ling Lu is at the Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China,

    Ling Lu

  2. John D. Joannopoulos and Marin Soljačić are in the Department of Physics, Massachusetts Institute of Technology, Cambridge 02139, USA,

    John D. Joannopoulos & Marin Soljačić

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  1. Ling Lu
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Correspondence to Ling Lu.

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Lu, L., Joannopoulos, J. & Soljačić, M. Topological states in photonic systems. Nature Phys 12, 626–629 (2016). https://doi.org/10.1038/nphys3796

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