Abstract

Weyl points have recently been predicted and experimentally observed in double-gyroid photonic crystals, as well as in other complex photonic structures such as stacked hexagonal-lattice slabs and helical waveguide arrays. In all above structures, the Weyl points are located between high frequency bands, and are difficult to probe experimentally. In this work, we show that a photonic crystal with a simple tetrahedral structure can host frequency-isolated Weyl points between the second and third bands. The minimal number of two Weyl points emerges from a threefold quadratic degeneracy at the Brillouin zone corner when time-reversal symmetry is broken. We verify theoretically that the Weyl points carry opposite topological charges, and are associated with Fermi arc-like surface states. This photonic crystal can be realized using ferromagnetic rods in the microwave frequency regime, providing a simple platform for studying the physics of Weyl points.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

Zhaoju Yang, Meng Xiao, Fei Gao, Ling Lu, Yidong Chong, and Baile Zhang, "Weyl points in a magnetic tetrahedral photonic crystal: erratum," Opt. Express 25, 23725-23725 (2017)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-25-20-23725

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References

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2016 (4)

W. J. Chen, M. Xiao, and C. T. Chan, “Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states,” Nat. Commun. 7, 13038 (2016).
[Crossref] [PubMed]

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Z. Yang and B. Zhang, “Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains,” Phys. Rev. Lett. 117(22), 224301 (2016).
[Crossref] [PubMed]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials,” Phys. Rev. Lett. 117(5), 057401 (2016).
[Crossref] [PubMed]

2015 (6)

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

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

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

2014 (1)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

2013 (2)

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

2011 (1)

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

2008 (1)

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

2001 (1)

1989 (1)

J. P. Bouchaud and P. G. Zérah, “Spontaneous resonances and universal behavior in ferrimagnets: Effective-medium theory,” Phys. Rev. Lett. 63(9), 1000–1003 (1989).
[Crossref] [PubMed]

Alidoust, N.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Bansil, A.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Belopolski, I.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Belotelov, V. I.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Béri, B.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Bernevig, B. A.

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Bian, G.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Bouchaud, J. P.

J. P. Bouchaud and P. G. Zérah, “Spontaneous resonances and universal behavior in ferrimagnets: Effective-medium theory,” Phys. Rev. Lett. 63(9), 1000–1003 (1989).
[Crossref] [PubMed]

Bravo-Abad, J.

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

Buljan, H.

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

Chan, C. T.

W. J. Chen, M. Xiao, and C. T. Chan, “Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states,” Nat. Commun. 7, 13038 (2016).
[Crossref] [PubMed]

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

Chang, G.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Chen, G. F.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Chen, W. J.

W. J. Chen, M. Xiao, and C. T. Chan, “Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states,” Nat. Commun. 7, 13038 (2016).
[Crossref] [PubMed]

Chen, W.-J.

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

Chin, J. Y.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Chou, F.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Dai, X.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Ding, H.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Dregely, D.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Fan, S.

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials,” Phys. Rev. Lett. 117(5), 057401 (2016).
[Crossref] [PubMed]

Fang, F.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Fang, Z.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Fu, B. B.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Fu, L.

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

Gao, W.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Giessen, H.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Gresch, D.

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Haldane, F. D.

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

Hasan, M. Z.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

He, W.-Y.

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

Huang, S.-M.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Huang, X. C.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Jia, S.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Joannopoulos, J.

Joannopoulos, J. D.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

Johnson, S.

Khanikaev, A. B.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Kivshar, Y. S.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Lawrence, M.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Lee, C.-C.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Lin, H.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Lin, Q.

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials,” Phys. Rev. Lett. 117(5), 057401 (2016).
[Crossref] [PubMed]

Lu, L.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

Lv, B. Q.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Ma, J.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Miao, H.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Mousavi, S. H.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Neupane, M.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Ni, X.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Qian, T.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Raghu, S.

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

Ran, L.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

Richard, P.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Sanchez, D. S.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Sankar, R.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Savrasov, S. Y.

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

Shibayev, P. P.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Slobozhanyuk, A.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Smirnova, D.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

Soljacic, M.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

Soluyanov, A. A.

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Steinle, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Stritzker, B.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Troyer, M.

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Turner, A. M.

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

Vishwanath, A.

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

Wan, X.

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

Wang, B.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Wang, X. P.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Wang, Z.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Wehlus, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Weiss, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

Weng, H. M.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Weyl, V. H.

V. H. Weyl, “Elektron und Gravitation. I.,” Z. Phys.56 (1929).

Wu, Q.

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Xiao, M.

W. J. Chen, M. Xiao, and C. T. Chan, “Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states,” Nat. Commun. 7, 13038 (2016).
[Crossref] [PubMed]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials,” Phys. Rev. Lett. 117(5), 057401 (2016).
[Crossref] [PubMed]

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

Xu, S.-Y.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Yang, B.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Yang, Z.

Z. Yang and B. Zhang, “Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains,” Phys. Rev. Lett. 117(22), 224301 (2016).
[Crossref] [PubMed]

Ye, D.

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

Yuan, Z.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Zérah, P. G.

J. P. Bouchaud and P. G. Zérah, “Spontaneous resonances and universal behavior in ferrimagnets: Effective-medium theory,” Phys. Rev. Lett. 63(9), 1000–1003 (1989).
[Crossref] [PubMed]

Zhang, B.

Z. Yang and B. Zhang, “Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains,” Phys. Rev. Lett. 117(22), 224301 (2016).
[Crossref] [PubMed]

Zhang, C.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

Zhang, S.

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Zhao, L. X.

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Zheng, H.

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

2D Materials (1)

J. Bravo-Abad, L. Lu, L. Fu, H. Buljan, and M. Soljačić, “Weyl points in photonic-crystal superlattices,” 2D Materials 2, 034013 (2015).

Nat. Commun. (3)

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, “Nonreciprocal plasmonics enables giant enhancement of thin-film Faraday rotation,” Nat. Commun. 4, 1599 (2013).
[Crossref] [PubMed]

W. J. Chen, M. Xiao, and C. T. Chan, “Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states,” Nat. Commun. 7, 13038 (2016).
[Crossref] [PubMed]

W. Gao, B. Yang, M. Lawrence, F. Fang, B. Béri, and S. Zhang, “Photonic Weyl degeneracies in magnetized plasma,” Nat. Commun. 7, 12435 (2016).
[Crossref] [PubMed]

Nat. Photonics (2)

L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nat. Photonics 7(4), 294–299 (2013).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, “Type-II Weyl semimetals,” Nature 527(7579), 495–498 (2015).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. B (1)

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

Phys. Rev. Lett. (4)

Z. Yang and B. Zhang, “Acoustic Type-II Weyl Nodes from Stacking Dimerized Chains,” Phys. Rev. Lett. 117(22), 224301 (2016).
[Crossref] [PubMed]

F. D. Haldane and S. Raghu, “Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry,” Phys. Rev. Lett. 100(1), 013904 (2008).
[Crossref] [PubMed]

M. Xiao, Q. Lin, and S. Fan, “Hyperbolic Weyl Point in Reciprocal Chiral Metamaterials,” Phys. Rev. Lett. 117(5), 057401 (2016).
[Crossref] [PubMed]

J. P. Bouchaud and P. G. Zérah, “Spontaneous resonances and universal behavior in ferrimagnets: Effective-medium theory,” Phys. Rev. Lett. 63(9), 1000–1003 (1989).
[Crossref] [PubMed]

Phys. Rev. X (1)

B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, “Experimental Discovery of Weyl Semimetal TaAs,” Phys. Rev. X 5, 031013 (2015).

Science (2)

S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, “Discovery of a Weyl fermion semimetal and topological Fermi arcs,” Science 349(6248), 613–617 (2015).
[Crossref] [PubMed]

L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Experimental observation of Weyl points,” Science 349(6248), 622–624 (2015).
[Crossref] [PubMed]

Other (5)

J. Noh, S. Huang, D. Leykam, Y. D. Chong, K. Chen, and M. C. Rechtsman, “Experimental observation of optical Weyl points,” arXiv 1610, 01033 (2016).

V. H. Weyl, “Elektron und Gravitation. I.,” Z. Phys.56 (1929).

A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (CRC Press, 1997).

L. Lu, and Z. Wang, “Topological one-way fiber of second Chern number,” arXiv 1611, 01998 (2016).

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat Photon advance online publication (2016).

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Figures (3)

Fig. 1
Fig. 1

Unit cell of the tetrahedral photonic crystal and Brillouin zone. (a) The unit cell consists of four rods of radius r = 0.13a. The rods point from (0, 0, 0) to (0.5, 0.5, 0.5), (−0.5, −0.5, 0.5), (0.5, −0.5, −0.5), (−0.5, 0.5, −0.5), respectively. (b) The cubic Brillouin zone of space group 208.

Fig. 2
Fig. 2

Band structure of the photonic crystal with and without magnetization. (a) Band structure without magnetization. (b) Band structure with magnetization along y direction. (c) The distribution the Weyl point in the first Brillouin zone. Red and Blue points represent Weyl points with opposite chirality.

Fig. 3
Fig. 3

The chirality and topological surface states. (a) The band structure in vicinity of the Weyl point at (0.50, 0.31, 0.50) with kz = 0.5. The frequency of degeneracy is 0.374×2πc/a. (b) The sphere in momentum space enclosing one Weyl point. The radius of the sphere is 0.05×2π/a. (c) The calculated Berry phase as a function of polar angle. The center of the sphere locates at the Weyl point (0.50, 0.31, 0.50). (d) The topologically protected surface state. (e) The photonic open arc (dark red dotted line) traced out from surface states at the fixed frequency 0.366×2πc/a in the surface Brillouin zone centered at R point.

Equations (1)

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ε=( ε xx 0 iκ 0 ε yy 0 iκ 0 ε zz ).

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