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We theoretically simulate one-photon and two-photon absorption spectra for monolayer and bilayer graphene employing the second-order perturbation theory of the electron-photon interaction. The tight-binding model is used to describe the band structure of graphene. The results show that one-photon absorption coefficient of monolayer graphene is a constant about 6.8×107 m-1, demonstrating that the absorptivity of incident light in monolayer graphene approximates to 2.3%. The one-photon absorption coefficient of bilayer graphene changes sectionally with the wavelength and is greater than that of monolayer graphene. The two-photon absorption coefficient of monolayer graphene is proportional to λ4. The two-photon absorption coefficient of bilayer graphene exhibits a giant resonance absorption peak in the infrared (～ 3100 nm) region. Our results will provide theoretical guidance for the application of graphene in the research field of optoelectronic devices.
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Keywords:
- graphene /
- optical absorption /
- tight-binding model
[1] 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
[2] 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
[3] Zhang Q H, Han J H, Feng G Y, Xu Q X, Ding L Z, Lu X X 2012 Acta Phys. Sin. 61 214209 (in Chinese) [张秋慧, 韩敬华, 冯国英, 徐其兴, 丁立中, 卢晓翔 2012 61 214209]
[4] Hu H X, Zhang Z H, Liu X H, Qiu M, Ding K H 2009 Acta Phys. Sin. 58 7156 (in Chinese) [胡海鑫, 张振华, 刘新海, 邱明, 丁开和 2009 58 7156]
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[6] Xu X G, Zhang C, Xu G J, Cao J C 2011 Chin. Phys. B 20 027201
[7] Zhao J, Zhang G Y, Shi D X 2013 Chin. Phys. B 22 057701
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[10] Min H, Sahu B, Banerjee S K, Mac-Donald A H 2007 Phys. Rev. B 75 155115
[11] Mak K F, Lui C H, Shan J, Heinz T F 2009 Phys. Rev. Lett. 102 256405
[12] Mucha-Kruczyński M, McCann E, Fal’ko V I 2010 Semicond. Sci. Technol. 25 033001
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[15] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
[16] Bao Q L, Zhang H, Wang Y, Ni Z H, Yan Y L, Shen Z X, Loh K P, Tang D Y 2009 Adv. Funct. Mater. 19 3077
[17] Xing G C, Guo H C, Zhang X H, Sum T C, Alfred Huan C H 2010 Opt. Express 18 4564
[18] Fan Y, Jiang Z G, Yao L F 2012 Chin. Opt. Lett. 10 071901
[19] Hendry E, Hale P J, Moger J, Savchenko A K 2010 Phys. Rev. Lett. 105 097401
[20] Zhang H, Virally S, Bao Q L, Ping L K, Massar S, Godbout N, Kockaert P 2012 Opt. Lett. 37 1856
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[22] Nilsson J, Castro Neto A H, Guinea F, Peres N M R 2008 Phys. Rev. B 78 045405
[23] Yin W H, Han Q, Yang X H 2012 Acta Phys. Sin. 61 248502 (in Chinese) [尹伟红, 韩勤, 杨晓红 2012 61 248502]
[24] Yang Z, Gao R G, Hu N, Chai J, Cheng Y W, Zhang L Y, Wei H, Kong E S W, Zhang Y F 2012 Nano-Micro Lett. 4 1
[25] Bonaccorso F, Sun Z, Hasan T, Ferrari1 A C 2010 Nature Photon. 4 611
[26] Nathan V, Guenther A H, Mitra S S 1985 J. Opt. Soc. Am. B 2 294
[27] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[28] Koshino M 2013 New J. Phys. 15 015010
[29] McCann E 2006 Phys. Rev. B 74 161403
[30] McCann E, Abergel D S L, Fal’ko V I 2007 Solid State Commun. 143 110
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[1] 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
[2] 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
[3] Zhang Q H, Han J H, Feng G Y, Xu Q X, Ding L Z, Lu X X 2012 Acta Phys. Sin. 61 214209 (in Chinese) [张秋慧, 韩敬华, 冯国英, 徐其兴, 丁立中, 卢晓翔 2012 61 214209]
[4] Hu H X, Zhang Z H, Liu X H, Qiu M, Ding K H 2009 Acta Phys. Sin. 58 7156 (in Chinese) [胡海鑫, 张振华, 刘新海, 邱明, 丁开和 2009 58 7156]
[5] Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M I, Novoselov K S 2007 Nat. Mater. 6 652
[6] Xu X G, Zhang C, Xu G J, Cao J C 2011 Chin. Phys. B 20 027201
[7] Zhao J, Zhang G Y, Shi D X 2013 Chin. Phys. B 22 057701
[8] Ouyang F P, Xu H, Wei C 2008 Acta Phys. Sin. 57 1073 (in Chinese) [欧阳方平, 徐慧, 魏辰 2008 57 1073]
[9] Toyoda T, Zhang C 2012 Phys. Lett. A 376 616
[10] Min H, Sahu B, Banerjee S K, Mac-Donald A H 2007 Phys. Rev. B 75 155115
[11] Mak K F, Lui C H, Shan J, Heinz T F 2009 Phys. Rev. Lett. 102 256405
[12] Mucha-Kruczyński M, McCann E, Fal’ko V I 2010 Semicond. Sci. Technol. 25 033001
[13] Rao C N R, Sood A K, Subrahmanyam K S, Govindaraj A 2009 Angewandte Chemie International Edition 48 7752
[14] Sarma S D, Shaffique A, Hwang E H, Enrico R 2011 Rev. Mod. Phys. 83 407
[15] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
[16] Bao Q L, Zhang H, Wang Y, Ni Z H, Yan Y L, Shen Z X, Loh K P, Tang D Y 2009 Adv. Funct. Mater. 19 3077
[17] Xing G C, Guo H C, Zhang X H, Sum T C, Alfred Huan C H 2010 Opt. Express 18 4564
[18] Fan Y, Jiang Z G, Yao L F 2012 Chin. Opt. Lett. 10 071901
[19] Hendry E, Hale P J, Moger J, Savchenko A K 2010 Phys. Rev. Lett. 105 097401
[20] Zhang H, Virally S, Bao Q L, Ping L K, Massar S, Godbout N, Kockaert P 2012 Opt. Lett. 37 1856
[21] Guinea F, Castro Neto A H, Peres N M R 2007 Solid State Commun. 143 116
[22] Nilsson J, Castro Neto A H, Guinea F, Peres N M R 2008 Phys. Rev. B 78 045405
[23] Yin W H, Han Q, Yang X H 2012 Acta Phys. Sin. 61 248502 (in Chinese) [尹伟红, 韩勤, 杨晓红 2012 61 248502]
[24] Yang Z, Gao R G, Hu N, Chai J, Cheng Y W, Zhang L Y, Wei H, Kong E S W, Zhang Y F 2012 Nano-Micro Lett. 4 1
[25] Bonaccorso F, Sun Z, Hasan T, Ferrari1 A C 2010 Nature Photon. 4 611
[26] Nathan V, Guenther A H, Mitra S S 1985 J. Opt. Soc. Am. B 2 294
[27] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[28] Koshino M 2013 New J. Phys. 15 015010
[29] McCann E 2006 Phys. Rev. B 74 161403
[30] McCann E, Abergel D S L, Fal’ko V I 2007 Solid State Commun. 143 110
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