Abstract
Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals—superlattices of metamaterials with judiciously designed properties—provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).
Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007).
Roy, R. Z2 classification of quantum spin Hall systems: An approach using time-reversal invariance. Phys. Rev. B 79, 195321 (2009).
Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X-L. & Zhang, S-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
König, M. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).
Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).
Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).
Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3, Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).
Lindner, N. l. H., Refael, G. & Galitski, V. Floquet topological insulators in semiconductor quantum wells. Nature Phys. 7, 490–495 (2011).
Haldane, F. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).
Wang, Z., Chong, Y., Joannopoulos, J. & Soljaćić, M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett. 100, 013905 (2008).
Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Phys. 7, 907–912 (2011).
Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000).
Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 305, 788–792 (2004).
Ulf, L. Optical conformal mapping. Science 312, 1777–1780 (2006).
Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).
Chen, H., Chan, C. T. & Sheng, P. Transformation optics and metamaterials. Nature Mater. 9, 387–396 (2010).
Veselago, V. G. The electrodynamics of substances with simultaneously negative values of permittivity and permeability. Soviet Phys. Usp. 10, 509–514 (1968).
Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).
Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).
Raghu, S. & Haldane, F. D. M. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834 (2008).
Fang, K., Yu, Z. & Fan, S. Microscopic theory of photonic one-way edge mode. Phys. Rev. B 84, 075477 (2011).
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljaćić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
Poo, Y., Wu, R., Lin, Z., Yang, Y. & Chan, C. T. Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett. 106, 093903 (2011).
Zharov, A. A., Shadrivov, I. V. & Kivshar, Y. S. Nonlinear properties of left-handed metamaterials. Phys. Rev. Lett. 91, 037401 (2003).
Klein, M. W., Enkrich, C., Wegener, M. & Linden, S. Second-harmonic generation from magnetic metamaterials. Science 313, 502–504 (2006).
Poutrina, E., Huang, D. & Smith, D. R. Analysis of nonlinear electromagnetic metamaterials. New J. Phys. 12, 093010 (2010).
Maciejko, J., Hughes, T. L. & Zhang, S-C. The quantum spin Hall effect. Annu. Rev. Condens. Matter Phys. 2, 31–53 (2011).
Kong, J. A. Theorems of bianisotropic media. Proc. IEEE 60, 1036–1046 (1972).
Serdyukov, A. N., Semchenko, I. V., Tretyakov, S. A. & Sihvola, A. Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).
Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors, and enhanced non-linear phenomena. Microw. Theory Technol. 47, 2075–2084 (1999).
Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001).
Marqués, R., Medina, F. & Rafii-El-Idrissi, R. Role of bianisotropy in negative permeability and left-handed metamaterials. Phys. Rev. B 65, 144440 (2002).
Rill, M. S. et al. Negative-index bianisotropic photonic metamaterial fabricated by direct laser writing and silver shadow evaporation. Opt. Lett. 34, 19–21 (2009).
Li, Z., Aydin, K. & Ozbay, E. Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients. Phys. Rev. E 79, 026610 (2009).
Saadoun, M. M. I. & Engheta, N. A reciprocal phase shifter using novel pseudochiral or ω medium. Microw. Opt. Technol. Lett. 5, 184–188 (1992).
Tretyakov, S. A., Simovski, C. R. & HudliÄŤka, M. Bianisotropic route to the realization and matching of backward-wave metamaterial slabs. Phys. Rev. B 75, 153104 (2007).
Tretyakov, S. A., Mariotte, F., Simovski, C. R., Kharina, T. G. & Heliot, J-P. Analytical antenna model for chiral scatterers: Comparison with numerical and experimental data. IEEE Trans. Antennas Propag. 44, 1006–1014 (1996).
Plum, E., Schwanecke, V. A. F., Zheludev, A. S. & Chen, N. I. Giant optical gyrotropy due to electromagnetic coupling. Appl. Phys. Lett. 90, 223113 (2007).
Gansel, J. K. et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).
Saenz, E. et al. Modeling of spirals with equal dielectric, magnetic, and chiral susceptibilities. Electromagnetics 28, 476–493 (2008).
Urzhumov, Y. A. & Shvets, G. Extreme anisotropy of wave propagation in two-dimensional photonic crystals. Phys. Rev. E 72, 026608 (2005).
Haldane, F. D. M. Model for a quantum Hall effect without landau levels: Condensed-matter realization of the parity anomaly. Phys. Rev. Lett. 61, 2015–2018 (1988).
Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).
Murakami, S., Nagaosa, N. & Zhang, S-C. Dissipationless quantum spin current at room temperature. Science 301, 1348–1351 (2003).
Sheng, D. N., Weng, Z. Y., Sheng, L. & Haldane, F. D. M. Quantum spin-Hall effect and topologically invariant Chern numbers. Phys. Rev. Lett. 97, 036808 (2006).
Acknowledgements
A.B.K., S.H.M. and G.S. acknowledge financial support from the Office of Naval Research grant N00014-10-1-0929 and the NSF award PHY-0851614. A.H.M. and W.K.T. acknowledge support from DOE Division of Materials Sciences and Engineering grant DE-FG03-02ER45958. M.K. acknowledges support from ARO grant W911NF-09-1-0527 and NSF grant DMR-0955778. G.S. acknowledges enlightening communications with M. Segev.
Author information
Authors and Affiliations
Contributions
All authors contributed extensively to the work presented in this paper.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Information (PDF 2117 kb)
Supplementary Information
Supplementary Movie S1 (AVI 6600 kb)
Supplementary Information
Supplementary Movie S2 (AVI 6600 kb)
Supplementary Information
Supplementary Movie S3 (AVI 32813 kb)
Supplementary Information
Supplementary Movie S4 (AVI 32813 kb)
Supplementary Information
Supplementary Movie S5 (AVI 32813 kb)
Supplementary Information
Supplementary Movie S6 (AVI 32813 kb)
Supplementary Information
Supplementary Movie S7 (AVI 32813 kb)
Supplementary Information
Supplementary Movie S8 (AVI 32813 kb)
Rights and permissions
About this article
Cite this article
Khanikaev, A., Hossein Mousavi, S., Tse, WK. et al. Photonic topological insulators. Nature Mater 12, 233–239 (2013). https://doi.org/10.1038/nmat3520
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nmat3520