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Dirac费米子作为粒子物理中的基本粒子之一，其理论在近年来蓬勃发展的拓扑电子理论领域中被广泛提及并用来刻画具有Dirac费米子性质的电子态.这种特殊的能态通常被称为Dirac点，在能谱上表现为两条不同能带之间的线性交叉点.由于Dirac点往往是发生拓扑相变的转变点，因而也被视为实现各种拓扑态的重要母态.作为可与拓扑电子体系类比的拓扑光子晶体因其独特的潜在应用价值也受到人们的广泛关注，实现包含Dirac点的光子能带已成为研究拓扑光子晶体的核心课题.本文基于电子的拓扑理论，简要地回顾了Dirac点在光子系统中的研究进展，特别介绍了如何在光子晶体中利用不同晶格对称性实现在高对称点/线上的Dirac点，以及由Dirac点衍生的Weyl点.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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[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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