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Experimental observation of optical Weyl points and Fermi arc-like surface states

Nature Physics volume 13, pages 611–617 (2017)Cite this article

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Abstract

Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called ‘Weyl points’, carry a topological charge and are therefore highly robust. There has been much excitement over recent observations of Weyl points in microwave photonic crystals and the semimetal TaAs. Here, we report on the experimental observation of ‘type-II’ Weyl points of light at optical frequencies, with the photons having a strictly positive group velocity along one spatial direction. We use a 3D structure consisting of laser-written waveguides, and show the presence of type-II Weyl points by observing conical diffraction along one axis when the frequency is tuned to the Weyl point; and observing the associated Fermi arc-like surface states. The realization of Weyl points at optical frequencies allows these novel electromagnetic modes to be further explored in the context of linear, nonlinear, and quantum optics.

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Figure 1: Schematic and corresponding band structure of a waveguide array that supports type-II Weyl points.
Figure 2: Theoretical and numerical demonstration of topological phase transition associated with type-II Weyl points.
Figure 3: Conical diffraction as a signature of the existence of type-II Weyl points.
Figure 4: Direct observation of Fermi arc-like surface states.

References

  1. Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  2. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    Article  ADS  Google Scholar 

  3. Lv, B. Q. et al. Experimental discovery of Weyl semimetal taas. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  4. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

    Article  ADS  Google Scholar 

  5. Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the quantized anomalous Hall effect in HGCr2Se4 . Phys. Rev. Lett. 107, 186806 (2011).

    Article  ADS  Google Scholar 

  6. Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).

    Article  ADS  Google Scholar 

  7. Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).

    Article  ADS  Google Scholar 

  8. Nieslen, H. B. & Ninomiya, M. The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130, 389–396 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  9. Burkov, A. A. Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27, 113201 (2015).

    Article  ADS  Google Scholar 

  10. Cho, G. Y., Bardarson, J. H., Lu, Y.-M. & Moore, J. E. Superconductivity of doped Weyl semimetals: finite-momentum pairing and electronic analog of the 3He-A phase. Phys. Rev. B 86, 214514 (2012).

    Article  ADS  Google Scholar 

  11. Bravo-Abad, J., Joannopoulos, J. D. & Soljacic, M. Enabling single-mode behavior over large areas with photonic Dirac cones. Proc. Natl Acad. Sci. USA 109, 9761–9765 (2012).

    Article  ADS  Google Scholar 

  12. Xu, Y., Zhang, F. & Zhang, C. Structured Weyl points in spin-orbit coupled fermionic superfluids. Phys. Rev. Lett. 115, 265304 (2015).

    Article  ADS  Google Scholar 

  13. Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

    Article  ADS  Google Scholar 

  14. Lu, L., Fu, L., Joannopoulos, J. D. & Soljačić, M. Weyl points and line nodes in gyroid photonic crystals. Nat. Photon. 7, 294–299 (2013).

    Article  ADS  Google Scholar 

  15. Wang, L., Jian, S.-K. & Yao, H. Topological photonic crystal with equifrequency Weyl points. Phys. Rev. A 93, 061801 (2016).

    Article  ADS  Google Scholar 

  16. Bravo-Abad, J., Lu, L., Fu, L., Buljan, H. & Soljačić, M. Weyl points in photonic-crystal superlattices. 2D Mater. 2, 034013 (2015).

    Article  Google Scholar 

  17. Gao, W. et al. Photonic Weyl degeneracies in magnetized plasma. Nat. Commun. 7, 12435 (2016).

    Article  ADS  Google Scholar 

  18. Xiao, M., Chen, W.-J., He, W.-Y. & Chan, C. T. Synthetic gauge flux and Weyl points in acoustic systems. Nat. Phys. 11, 920–924 (2015).

    Article  Google Scholar 

  19. Yang, Z. & Zhang, B. Acoustic Weyl nodes from stacking dimerized chains. Phys. Rev. Lett. 117, 224301 (2016).

    Article  ADS  Google Scholar 

  20. Xiao, M., Lin, Q. & Fan, S. Hyperbolic Weyl point in reciprocal chiral metamaterials. Phys. Rev. Lett. 117, 057401 (2016).

    Article  ADS  Google Scholar 

  21. Chen, W.-J., Xiao, M. & Chan, C. Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states. Nat. Commun. 7, 13038 (2016).

    Article  ADS  Google Scholar 

  22. Peng, S. et al. Three-dimensional single gyroid photonic crystals with a mid-infrared bandgap. ACS Photon. 3, 1131–1137 (2016).

    Article  Google Scholar 

  23. Peng, S. et al. Gyroid photonic crystal with Weyl points: synthesis and mid-infrared photonic characterization. APS March Meeting 2016, Abstract #S52.013 (2016).

  24. Xiao, M., Lin, Q. & Fan, S. Hyperbolic Weyl point in reciprocal chiral metamaterials. Phys. Rev. Lett. 117, 057401 (2016).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  26. Yariv, A. & Yeh, P. Optical Waves in Crystals Vol. 10 (Wiley, 1984).

    Google Scholar 

  27. Fleischer, J. W., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003).

    Article  ADS  Google Scholar 

  28. Leykam, D., Rechtsman, M. C. & Chong, Y. D. Anomalous topological phases and unpaired Dirac cones in photonic Floquet topological insulators. Phys. Rev. Lett. 117, 013902 (2016).

    Article  ADS  Google Scholar 

  29. 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).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Berry, M., Jeffrey, M. & Lunney, J. Conical diffraction: observations and theory. Proc. R. Soc. A 462, 1629–1642 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  32. Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007).

    Article  ADS  Google Scholar 

  33. Kim, Y., Wieder, B. J., Kane, C. L. & Rappe, A. M. Dirac line nodes in inversion-symmetric crystals. Phys. Rev. Lett. 115, 036806 (2015).

    Article  ADS  Google Scholar 

  34. Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901 (2016).

    Article  ADS  Google Scholar 

  35. Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).

    Article  ADS  Google Scholar 

  36. Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).

    Article  ADS  Google Scholar 

  37. Rechtsman, M. C. et al. Topological protection of photonic path entanglement. Optica 3, 925–930 (2016).

    Article  Google Scholar 

Download references

Acknowledgements

M.C.R. acknowledges the National Science Foundation under award number ECCS-1509546, the Penn State MRSEC, Center for Nanoscale Science, under award number NSF DMR-1420620, and the Alfred P. Sloan Foundation under fellowship number FG-2016-6418. K.P.C. acknowledges the National Science Foundation under award numbers ECCS-1509199 and DMS-1620218. D.L. and C.Y.D. acknowledge support by the Singapore National Research Foundation under grant No. NRFF2012-02, by the Singapore MOE Academic Research Fund Tier 2 Grant No. MOE2015-T2-2-008, and by the Singapore MOE Academic Research Fund Tier 3 grant MOE2011-T3-1-005.

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Author notes

  1. Jiho Noh, Sheng Huang and Daniel Leykam: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

    Jiho Noh & Mikael C. Rechtsman

  2. Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA

    Sheng Huang & Kevin P. Chen

  3. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore

    Daniel Leykam & Y. D. Chong

  4. Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore

    Y. D. Chong

Authors
  1. Jiho Noh
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  2. Sheng Huang
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  3. Daniel Leykam
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  4. Y. D. Chong
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  5. Kevin P. Chen
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  6. Mikael C. Rechtsman
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Contributions

J.N. carried out experimental measurements and performed the data analysis; S.H. developed the laser fabrication process and characterized the samples under the supervision of K.P.C. and with guidance from M.C.R.; D.L., C.Y.D. and M.C.R. conceived the idea and performed theoretical analysis and calculations; M.C.R. supervised the project.

Corresponding author

Correspondence to Mikael C. Rechtsman.

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Noh, J., Huang, S., Leykam, D. et al. Experimental observation of optical Weyl points and Fermi arc-like surface states . Nature Phys 13, 611–617 (2017). https://doi.org/10.1038/nphys4072

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