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In this paper, we present a detailed theoretical study of nonlinear terahertz optical properties of graphene in the presence of electric field and terahertz radiation field. The optical current is computed and investigated on the basis of quantum theory and semi-classical Boltzmann equations. It shows a large nonlinear terahertz response and the nonlinearity becomes larger with increasing electric field or decreasing terahertz frequencies. Moreover, it is found that the optical nonlinearity can be modified and controlled by electric fields.
[1] Quhe R G, Zheng J X, Luo G F, Liu Q H, Qin R, Zhou J, Yu D P, Nagase S, Mei W N, Gao Z X, Lu J 2012 NPG Asia Materials 4 e6
[2] Wu H Q, Linghu C Y, L H M, Qian H 2013 Chin. Phys. B 22 098106
[3] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[4] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[5] Yuan W J, Liu A R, Huang L, Li C, Shi G Q 2013 Advanced Materials 25 766
[6] Guinea F, Katsnelson M I, Geim A K 2010 Nature Physics 6 30
[7] Eda G, Fanchini G, Chhowalla M 2008 Nature Nanotechnol 3 270
[8] Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P, Stormer H L, Basov D N 2008 Nature Physics 4 532
[9] Hendry E, Hale P J, Moger J, Savchenko A K, Mikhailov S A 2010 Phys. Rev. Lett. 105 097401
[10] Lu J J, Feng M, Zhan H B 2013 Acta Phys. Sin. 62 014204 (in Chinese) [陆晶晶, 冯苗, 詹红兵 2013 物理学报 62 014204]
[11] Zuo Z G, Wang P, Ling F R, Liu J S, Yao J Q 2013 Chin. Phys. B 22 097304
[12] Zhang H, Tang D Y, Knize R J, Zhao L M, Bao Q L, Loh K P 2010 Appl. Phys. Lett. 96 111112
[13] Wright A R, Xu X G, Cao J C, Zhang C 2009 Appl. Phys. Lett. 95 072101
[14] Ishikawa K L 2010 Phys. Rev. B 82 201402(R)
[15] Dong H M, Xu W, Zeng Z, Lu T C, Peeters F M 2008 Phys. Rev. B 77 235402
[16] Dong H M, Xu W, Peeters F M 2011 Jounal of Applied Physics 110 063704
[17] Dong H M, Xu W, Zhang J, Yuan Y Z 2010 Optics Communications 283 3695
[18] Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304
[19] Chen Y L, Feng X B, Hong D D 2013 Acta Phys. Sin. 62 187301 (in Chinese) [陈英良, 冯小波, 侯德东 2013 物理学报 62 187301]
[20] Haus H A, Wong W S 1996 Rev. Mod. Phys. 68 423
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[1] Quhe R G, Zheng J X, Luo G F, Liu Q H, Qin R, Zhou J, Yu D P, Nagase S, Mei W N, Gao Z X, Lu J 2012 NPG Asia Materials 4 e6
[2] Wu H Q, Linghu C Y, L H M, Qian H 2013 Chin. Phys. B 22 098106
[3] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[4] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[5] Yuan W J, Liu A R, Huang L, Li C, Shi G Q 2013 Advanced Materials 25 766
[6] Guinea F, Katsnelson M I, Geim A K 2010 Nature Physics 6 30
[7] Eda G, Fanchini G, Chhowalla M 2008 Nature Nanotechnol 3 270
[8] Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P, Stormer H L, Basov D N 2008 Nature Physics 4 532
[9] Hendry E, Hale P J, Moger J, Savchenko A K, Mikhailov S A 2010 Phys. Rev. Lett. 105 097401
[10] Lu J J, Feng M, Zhan H B 2013 Acta Phys. Sin. 62 014204 (in Chinese) [陆晶晶, 冯苗, 詹红兵 2013 物理学报 62 014204]
[11] Zuo Z G, Wang P, Ling F R, Liu J S, Yao J Q 2013 Chin. Phys. B 22 097304
[12] Zhang H, Tang D Y, Knize R J, Zhao L M, Bao Q L, Loh K P 2010 Appl. Phys. Lett. 96 111112
[13] Wright A R, Xu X G, Cao J C, Zhang C 2009 Appl. Phys. Lett. 95 072101
[14] Ishikawa K L 2010 Phys. Rev. B 82 201402(R)
[15] Dong H M, Xu W, Zeng Z, Lu T C, Peeters F M 2008 Phys. Rev. B 77 235402
[16] Dong H M, Xu W, Peeters F M 2011 Jounal of Applied Physics 110 063704
[17] Dong H M, Xu W, Zhang J, Yuan Y Z 2010 Optics Communications 283 3695
[18] Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304
[19] Chen Y L, Feng X B, Hong D D 2013 Acta Phys. Sin. 62 187301 (in Chinese) [陈英良, 冯小波, 侯德东 2013 物理学报 62 187301]
[20] Haus H A, Wong W S 1996 Rev. Mod. Phys. 68 423
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