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Dirac Fermion, as one of the basic particles in the particle physics, nowadays have been widely used to describe the electronic states with the behavior of Dirac fermion in the topological electronics. These exotic electronic states are called Dirac point, which exhibited as a linear crossing point in the band structure. Usually Dirac point is the topological phase transition point and thus viewed as the mother state of various topological states. As an analogue of topological electronics, topological photonics, also attracted a great deal of interest due to its potential application. One of the key topic in topological photonics is to realize photonic bands with Dirac point. In this review, we briefly introduce the progress of Dirac point in the photonic system and focus on the realization method of Dirac point in photonic crystal by take advantage of lattice symmetry. We also discuss Weyl point in the photonic crystal as an extension of the Dirac point.
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Keywords:
- photonic crystal /
- Dirac point /
- topological band /
- quantum spin Hall effect
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[27] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
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[29] Yang B J, Nagaosa N 2014 Nat. Commun. 5 4898
[30] Yang B J, Morimoto T, Furusaki A 2015 Phys. Rev. B 92 165120
[31] Lu L, Joannopoulos J D, Soljacic M 2013 Nat. Photon. 7 294
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[1] Dirac P A M 1928 Proc. R. Soc. London A 118 351
[2] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[3] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Scinece 315 1379
[4] Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620
[5] Shen S Q 1988 Phys. Rev. Lett. 61 2015
[6] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[7] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
[8] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[9] Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803
[10] Weyl H Z 1929 Physik 56 330
[11] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
[12] Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2008 Phys. Rev. Lett. 100 013905
[13] Ao X Y, Lin Z F, Chan C T 2009 Phys. Rev. B 80 033105
[14] Khanikaev A B, Hossein M S, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233
[15] Ma T, Khanikaev A B, Hossein M S, Shvets G 2015 Phys. Rev. Lett. 114 127401
[16] Chen W J, Jiang S J, Chen X D, Zhu B C, Zhou L, Dong J W, Chen C T 2014 Nat. Commun. 5 5782
[17] He C, Sun X C, Liu X P, Lu M H, Chen Y L, Feng L, ChenY F 2016 Proc. Natl. Acad. Sci. USA 113 4924
[18] Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901
[19] Sabyaschi B, Hirokazu M, Wade D, Edo E, Mohammad H 2016 New J. Phys. 18 113013
[20] Xu L, Wang H X, Xu Y D, Chen H Y, Jiang J H 2016 Opt. Express 24 18059
[21] Wang H X, Xu L, Chen H Y, Jiang J H 2016 Phys. Rev. B 93 235155
[22] Wang H X, Chen Y G, Hang Z H, Kee H Y, Jiang J H 2017 npj Quantum Materials 2 54
[23] Sakoda K 2012 Opt. Express 20 25181
[24] Sakoda K 2012 Opt. Express 20 25181
[25] Mcphedran R C, Nicorovici N A, Mckenzie D R, Botten L C, Parker A R, Rouse G W 2001 Aust. J. Chem. 54 241
[26] Sanders J V 1964 Nature 204 1151
[27] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[28] Lidorikis E, Sigalas M M, Economou E N, Soukoulis C M 1998 Phys. Rev. Lett. 81 1405
[29] Yang B J, Nagaosa N 2014 Nat. Commun. 5 4898
[30] Yang B J, Morimoto T, Furusaki A 2015 Phys. Rev. B 92 165120
[31] Lu L, Joannopoulos J D, Soljacic M 2013 Nat. Photon. 7 294
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