搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

石墨烯超快动态光学性质

金芹 董海明 韩奎 王雪峰

引用本文:
Citation:

石墨烯超快动态光学性质

金芹, 董海明, 韩奎, 王雪峰

Ultrafast dynamic optical properties of graphene

Jin Qin, Dong Hai-Ming, Han Kui, Wang Xue-Feng
PDF
导出引用
  • 通过建立石墨烯的光学布洛赫方程, 研究了弱光场下的单层石墨烯超快动态光学性质. 理论研究表明在太赫兹辐射光场下由于泡利不相容和能量守恒原理使得石墨烯系统建立动态非平衡载流子并达到饱和的时间是20200 fs, 能够在1 ps之内迅速产生光电流. 研究发现2evF E0 tħ是石墨烯线性光学响应区; 否则是石墨烯系统非线性光学响应区, E0 和 分别对应入射光的强度和频率, t为时间, vF是石墨烯狄拉克点附近电子的费米速度. 研究发现光子能量ħ越大, 电极化强度以及光电流越强. 我们的理论研究结果与已有的众多实验结果一致, 表明石墨烯在超快动态光学领域尤其是太赫兹领域拥有重要的研究和应用价值.
    Graphene exhibits excellent ultrafast optical properties due to its unique electronic structure. In this paper we investigate theoretically the ultrafast dynamic optical properties of graphene based on the Bloch-equations, and introduce the theoretical model of graphene. First, we give the energy which has a linear relationship with the wave vector k. The behavior of electrons in the vicinity of the two Dirac points can be described by the massless Dirac-equation, thus we have the Dirac equation of graphene. Second, we discuss the interaction between graphene and light field. The Bloch-equations of graphene are obtained through the Heisenberg equation and then we discuss the photon carriers,electric polarization and optical current change over time by analyzing the Bloch-equations. It is found that the nonequilibrium carriers in graphene induced by a terahertz field can be built in 20-200 fs due to the Pauli blocking and the conservation of energy principle. The photon carrier density will increase with the frequency of enhanced light field. Thus an optical current can be created rapidly within 1 ps. A graphene system responds linearly to the external optical field for 2evFE0tħ, while the graphene systems respond nonlinearly to the external optical field, where E0 and are respectively the intensity and the frequency of the light, t is the time and vF the Dirac velocity in graphene. The electric polarization and optical current increase with increasing photon energies. These theoretical results are in agreement with recent experimental findings and indicate that graphene exhibits important features and has practical applications in the ultrafast optic filed, especially in terahertz field.
      通信作者: 董海明, hmdong@cumt.edu.cn
    • 基金项目: 中央高校基本科研业务费专项基金(批准号: 2013QNA29)和国家自然科学基金(批准号: 11247002)资助的课题.
      Corresponding author: Dong Hai-Ming, hmdong@cumt.edu.cn
    • Funds: Project supported by the Fundamental Research Funds for the Central Universities of Ministry (Grant No.2013QNA29), and by the National Natural Science Foundation of China (Grant No. 11247002).
    [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, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Science 102 10451

    [3]

    Geim A K, MacDonald A H 2007 Phys. Today 60 35

    [4]

    Williams J R, Di C L, Marcus C M 2007 Science 317 638

    [5]

    Nomura K, Mac A H 2006 Phys. Rev. Lett. 96 6602

    [6]

    Brink J 2007 Nat. Nanotechnol. 2 199

    [7]

    Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201

    [8]

    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 Science 315 1379

    [9]

    Heersche H B, Jarillo H P, Oostinga J B, Vandersypen L M K, Morpurgo A F 2007 Solid State Commun 143 72

    [10]

    Vozmediano M A H, Lopez-Saneho M P, Stauber T, Guinea F 2005 Phys. Rev. B 72 5121

    [11]

    Dragoman M, Dragoman D, Deligiorgis G, Konstantinidis G, Neculoiu D, Cismaru A, Plana R 2009 J. Appl. Phys. 106 044312

    [12]

    Xia F N, Mueller T, Lin Y M, Valdes-Garcia A, Avouris P 2009 Nat. Nanotechnol. 4 839

    [13]

    Kim K, Choi J Y, Kim T, Cho S H, Chung H J 2011 Nature 479 338

    [14]

    Fang Z Y, Wang Y M, Schlather A E, Liu Z, Ajayan P M, F. Javier Garcia de Abajo, Nordlander P, Zhu X, Halas N J 2014 Nano Lett. 14 299

    [15]

    Fang Z Y, Liu Z, Wang Y M, Ajayan P M, Nordlander P, Halas N J 2012 Nano Letters 12 3808

    [16]

    Fang Z Y, Thongrattanasiri S, Schlather A, Liu Z, Ma L L, Wang Y M, Ajayan P M, Nordlander P, Halas N J, F. v Javier Garc. ade Abajo 2013 ACS Nano 7 2388

    [17]

    Yan B, Yang X X, Fang J Y, Huang Y D, Qin H, Qin S Q 2015 Chin. Phys. B 24 015023

    [18]

    Hendry E, Hale P J, Moger J and Savchenko A K 2010 Phys. Rev. Lett. 105 097401

    [19]

    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

    [20]

    Ruzicka B A, Wang S, Liu J W, Loh K P, Wu J Z, Zhao H 2012 Optics Materials Express 2 708

    [21]

    Dawlaty J M, Shivaraman S, Chandrashekhar M, Rana F, Spencer M G 2008 Applied Physics Letters 92 042116

    [22]

    Liu Z B, Zhao X, Zhang X L, Yan X Q, Wu Y P, Chen Y S, Tian J G 2011 The Journal of Physical Chemistry Letters 2 1972

    [23]

    Xing G H, Guo H C, Zhang X H, Sum T C, Huan C H A 2010 Optics Express 18 4564

    [24]

    Brida D, Manzoni C, Cerullo G, Tomadin A, Polini M, Nair R R, Geim A K, Novoselov K S, Milana S, Lombardo A, Ferrari A C 2012 Conference on Lasers and Electro-Optics San Jose, California United States, May 60-11, 2012 pQTh3H.1

    [25]

    Sun D, Divin C, Mihnev M, Winzer T, Malic E, Knorr A, Sipe J E, Berger C, Heer W A D, First P N, Norris T B 2012 New Journal of Physics 14 105012

    [26]

    Søren Ulstrup, Johannsen J C, Crepaldi A, Cilento F, Zacchigna M, Cacho C, Chapman R T, Springate E, Fromm F, Raidel C, Seyller T, Parmigiani F, Grioni M Hofmann P 2015 J. Phys.: Condensed Matter 27 164206

    [27]

    Liu M, Yin X B, Ulin-Avila E, Geng B S, Zentgraf T, Ju L, Wang F, Zhang X 2011 Nature 474 64

    [28]

    Breusing M, Kuehn S, Winzer T, Malic E, Milde F, Severin N, Rabe J P, Ropers C, Knorr A, Elsaesser T 2011 Phys. Rev. B 83 153410

    [29]

    Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304

    [30]

    Dong H M, Han K, Xu W 2014 Journal of Applied Physics 115 063503

    [31]

    Dong H M 2013 Acta Phys. Sin. 62 237804 (in Chinese) [董海明 2013 物理学报 62 237804]

    [32]

    Ang Y S, Chen Q J, Zhang C 2015 Front. Optoelectron. 8 3

  • [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, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Science 102 10451

    [3]

    Geim A K, MacDonald A H 2007 Phys. Today 60 35

    [4]

    Williams J R, Di C L, Marcus C M 2007 Science 317 638

    [5]

    Nomura K, Mac A H 2006 Phys. Rev. Lett. 96 6602

    [6]

    Brink J 2007 Nat. Nanotechnol. 2 199

    [7]

    Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201

    [8]

    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 Science 315 1379

    [9]

    Heersche H B, Jarillo H P, Oostinga J B, Vandersypen L M K, Morpurgo A F 2007 Solid State Commun 143 72

    [10]

    Vozmediano M A H, Lopez-Saneho M P, Stauber T, Guinea F 2005 Phys. Rev. B 72 5121

    [11]

    Dragoman M, Dragoman D, Deligiorgis G, Konstantinidis G, Neculoiu D, Cismaru A, Plana R 2009 J. Appl. Phys. 106 044312

    [12]

    Xia F N, Mueller T, Lin Y M, Valdes-Garcia A, Avouris P 2009 Nat. Nanotechnol. 4 839

    [13]

    Kim K, Choi J Y, Kim T, Cho S H, Chung H J 2011 Nature 479 338

    [14]

    Fang Z Y, Wang Y M, Schlather A E, Liu Z, Ajayan P M, F. Javier Garcia de Abajo, Nordlander P, Zhu X, Halas N J 2014 Nano Lett. 14 299

    [15]

    Fang Z Y, Liu Z, Wang Y M, Ajayan P M, Nordlander P, Halas N J 2012 Nano Letters 12 3808

    [16]

    Fang Z Y, Thongrattanasiri S, Schlather A, Liu Z, Ma L L, Wang Y M, Ajayan P M, Nordlander P, Halas N J, F. v Javier Garc. ade Abajo 2013 ACS Nano 7 2388

    [17]

    Yan B, Yang X X, Fang J Y, Huang Y D, Qin H, Qin S Q 2015 Chin. Phys. B 24 015023

    [18]

    Hendry E, Hale P J, Moger J and Savchenko A K 2010 Phys. Rev. Lett. 105 097401

    [19]

    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

    [20]

    Ruzicka B A, Wang S, Liu J W, Loh K P, Wu J Z, Zhao H 2012 Optics Materials Express 2 708

    [21]

    Dawlaty J M, Shivaraman S, Chandrashekhar M, Rana F, Spencer M G 2008 Applied Physics Letters 92 042116

    [22]

    Liu Z B, Zhao X, Zhang X L, Yan X Q, Wu Y P, Chen Y S, Tian J G 2011 The Journal of Physical Chemistry Letters 2 1972

    [23]

    Xing G H, Guo H C, Zhang X H, Sum T C, Huan C H A 2010 Optics Express 18 4564

    [24]

    Brida D, Manzoni C, Cerullo G, Tomadin A, Polini M, Nair R R, Geim A K, Novoselov K S, Milana S, Lombardo A, Ferrari A C 2012 Conference on Lasers and Electro-Optics San Jose, California United States, May 60-11, 2012 pQTh3H.1

    [25]

    Sun D, Divin C, Mihnev M, Winzer T, Malic E, Knorr A, Sipe J E, Berger C, Heer W A D, First P N, Norris T B 2012 New Journal of Physics 14 105012

    [26]

    Søren Ulstrup, Johannsen J C, Crepaldi A, Cilento F, Zacchigna M, Cacho C, Chapman R T, Springate E, Fromm F, Raidel C, Seyller T, Parmigiani F, Grioni M Hofmann P 2015 J. Phys.: Condensed Matter 27 164206

    [27]

    Liu M, Yin X B, Ulin-Avila E, Geng B S, Zentgraf T, Ju L, Wang F, Zhang X 2011 Nature 474 64

    [28]

    Breusing M, Kuehn S, Winzer T, Malic E, Milde F, Severin N, Rabe J P, Ropers C, Knorr A, Elsaesser T 2011 Phys. Rev. B 83 153410

    [29]

    Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304

    [30]

    Dong H M, Han K, Xu W 2014 Journal of Applied Physics 115 063503

    [31]

    Dong H M 2013 Acta Phys. Sin. 62 237804 (in Chinese) [董海明 2013 物理学报 62 237804]

    [32]

    Ang Y S, Chen Q J, Zhang C 2015 Front. Optoelectron. 8 3

  • [1] 崔磊, 刘洪梅, 任重丹, 杨柳, 田宏玉, 汪萨克. 石墨烯线缺陷局域形变对谷输运性质的影响. 物理学报, 2023, 72(16): 166101. doi: 10.7498/aps.72.20230736
    [2] 詹真, 张亚磊, 袁声军. 石墨烯莫尔超晶格的晶格弛豫与衬底效应. 物理学报, 2022, 71(18): 187302. doi: 10.7498/aps.71.20220872
    [3] 李海鹏, 周佳升, 吉炜, 杨自强, 丁慧敏, 张子韬, 沈晓鹏, 韩奎. 边界对石墨烯量子点非线性光学性质的影响. 物理学报, 2021, 70(5): 057801. doi: 10.7498/aps.70.20201643
    [4] 吕新宇, 李志强. 石墨烯莫尔超晶格体系的拓扑性质及光学研究进展. 物理学报, 2019, 68(22): 220303. doi: 10.7498/aps.68.20191317
    [5] 林奎鑫, 李多生, 叶寅, 江五贵, 叶志国, Qinghua Qin, 邹伟. 扭转双层石墨烯物理性质、制备方法及其应用的研究进展. 物理学报, 2018, 67(24): 246802. doi: 10.7498/aps.67.20181432
    [6] 李小兵, 陆卫兵, 刘震国, 陈昊. 基于可调石墨烯超表面的宽角度动态波束控制. 物理学报, 2018, 67(18): 184101. doi: 10.7498/aps.67.20180592
    [7] 闫昕, 梁兰菊, 张璋, 杨茂生, 韦德泉, 王猛, 李院平, 吕依颖, 张兴坊, 丁欣, 姚建铨. 基于石墨烯编码超构材料的太赫兹波束多功能动态调控. 物理学报, 2018, 67(11): 118102. doi: 10.7498/aps.67.20180125
    [8] 王功长, 魏凯, 李岩. 基于布洛赫方程的多色信标回波光子数数值仿真. 物理学报, 2018, 67(5): 054204. doi: 10.7498/aps.67.20171940
    [9] 张银, 冯一军, 姜田, 曹杰, 赵俊明, 朱博. 基于石墨烯的太赫兹波散射可调谐超表面. 物理学报, 2017, 66(20): 204101. doi: 10.7498/aps.66.204101
    [10] 张婷婷, 成蒙, 杨蓉, 张广宇. 锯齿形石墨烯反点网络加工与输运性质研究. 物理学报, 2017, 66(21): 216103. doi: 10.7498/aps.66.216103
    [11] 范达志, 刘贵立, 卫琳. 扭转形变对石墨烯吸附O原子电学和光学性质影响的电子理论研究. 物理学报, 2017, 66(24): 246301. doi: 10.7498/aps.66.246301
    [12] 张会云, 黄晓燕, 陈琦, 丁春峰, 李彤彤, 吕欢欢, 徐世林, 张晓, 张玉萍, 姚建铨. 基于石墨烯互补超表面的可调谐太赫兹吸波体. 物理学报, 2016, 65(1): 018101. doi: 10.7498/aps.65.018101
    [13] 禹忠, 党忠, 柯熙政, 崔真. N/B掺杂石墨烯的光学与电学性质. 物理学报, 2016, 65(24): 248103. doi: 10.7498/aps.65.248103
    [14] 卢晓波, 张广宇. 石墨烯莫尔超晶格. 物理学报, 2015, 64(7): 077305. doi: 10.7498/aps.64.077305
    [15] 黄向前, 林陈昉, 尹秀丽, 赵汝光, 王恩哥, 胡宗海. 一维石墨烯超晶格上的氢吸附. 物理学报, 2014, 63(19): 197301. doi: 10.7498/aps.63.197301
    [16] 叶振强, 曹炳阳, 过增元. 石墨烯的声子热学性质研究. 物理学报, 2014, 63(15): 154704. doi: 10.7498/aps.63.154704
    [17] 董海明. 掺杂石墨烯系统电场调控的非线性太赫兹光学特性研究. 物理学报, 2013, 62(23): 237804. doi: 10.7498/aps.62.237804
    [18] 陈英良, 冯小波, 侯德东. 单层与双层石墨烯的光学吸收性质研究. 物理学报, 2013, 62(18): 187301. doi: 10.7498/aps.62.187301
    [19] 姚志东, 李炜, 高先龙. 点缺陷扶手型石墨烯量子点的电子性质研究. 物理学报, 2012, 61(11): 117105. doi: 10.7498/aps.61.117105
    [20] 冯现徉, 逯瑶, 蒋雷, 张国莲, 张昌文, 王培吉. In掺杂ZnO超晶格光学性质的研究. 物理学报, 2012, 61(5): 057101. doi: 10.7498/aps.61.057101
计量
  • 文章访问数:  5627
  • PDF下载量:  367
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-06-30
  • 修回日期:  2015-08-15
  • 刊出日期:  2015-12-05

/

返回文章
返回