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We found that core-shell gyromagnetic photonic crystal of two-dimensional triangular lattice exhibit topological phases. In a certain parameters and magnetic field, those phases could be a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase. Different from the structure of Ref[1], phase transitions in our core-shell structure does not involve changes of space symmetry, which depend on parameters of our structure and the broken of time reverse symmetry. Our result shows the variety of topological phase transitions in photonic crystals.
[1] Chen Z G, Mei J, Sun X C, Zhang X, Zhao J, Wu Y 2017 Phys. Rev. A 95 043827
[2] Hall E H 1879 Am. J. Math. 2 287
[3] Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[4] Thouless D, Kohmoto M, Nightingale M, den Nijs M 1982 Phys. Rev. Lett. 49 405
[5] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[6] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[7] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[8] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[9] Fu L 2011 Phys. Rev. Lett. 106 106802
[10] Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490
[11] Haldane F, Raghu S 2008 Phys. Rev. Lett. 100 013904
[12] Raghu S, Haldane F 2008 Phys. Rev. A. 78 033834
[13] Lu L, Joannopoulos J D, Soljačić M 2014 Nat. Photon. 8 821
[14] Wang Z, Chong Y, Joannopoulos J, Soljačić M 2009 Nature 461 772
[15] Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905
[16] Chen W J, Jiang S J, Chen X D, Zhu B, Zhou L, Dong J W, Chan C 2014 Nat. Commun. 5 5782
[17] Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233
[18] Ma T, Khanikaev A B, Mousavi S H, Shvets G 2015 Phys. Rev. Lett. 114 127401
[19] Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901
[20] Xu L, Wang H X, Xu Y D, Chen H Y, Jiang J H 2016 Opt. Express 24 18059
[21] Pozar D M 2009 Microwave Engineering (Hoboken: John Wiley Sons)
[22] Sakoda K 2004 Optical Properties of Photonic Crystals (Berlin: Springer Science Business Media)
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[1] Chen Z G, Mei J, Sun X C, Zhang X, Zhao J, Wu Y 2017 Phys. Rev. A 95 043827
[2] Hall E H 1879 Am. J. Math. 2 287
[3] Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494
[4] Thouless D, Kohmoto M, Nightingale M, den Nijs M 1982 Phys. Rev. Lett. 49 405
[5] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[6] Xiao D, Chang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[7] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
[8] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757
[9] Fu L 2011 Phys. Rev. Lett. 106 106802
[10] Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490
[11] Haldane F, Raghu S 2008 Phys. Rev. Lett. 100 013904
[12] Raghu S, Haldane F 2008 Phys. Rev. A. 78 033834
[13] Lu L, Joannopoulos J D, Soljačić M 2014 Nat. Photon. 8 821
[14] Wang Z, Chong Y, Joannopoulos J, Soljačić M 2009 Nature 461 772
[15] Wang Z, Chong Y, Joannopoulos J D, Soljačić M 2008 Phys. Rev. Lett. 100 013905
[16] Chen W J, Jiang S J, Chen X D, Zhu B, Zhou L, Dong J W, Chan C 2014 Nat. Commun. 5 5782
[17] Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G 2013 Nat. Mater. 12 233
[18] Ma T, Khanikaev A B, Mousavi S H, Shvets G 2015 Phys. Rev. Lett. 114 127401
[19] Wu L H, Hu X 2015 Phys. Rev. Lett. 114 223901
[20] Xu L, Wang H X, Xu Y D, Chen H Y, Jiang J H 2016 Opt. Express 24 18059
[21] Pozar D M 2009 Microwave Engineering (Hoboken: John Wiley Sons)
[22] Sakoda K 2004 Optical Properties of Photonic Crystals (Berlin: Springer Science Business Media)
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