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原子错位堆栈增强双层MoS2高次谐波产率

姚惠东 崔波 马思琦 余超 陆瑞锋

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原子错位堆栈增强双层MoS2高次谐波产率

姚惠东, 崔波, 马思琦, 余超, 陆瑞锋

Enhancing high harmonic generation in bilayer MoS2 by interlayer atomic dislocation

Yao Hui-Dong, Cui Bo, Ma Si-Qi, Yu Chao, Lu Rui-Feng
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  • 本文采用数值求解多能带半导体布洛赫方程组的方法开展强激光与双层MoS2材料相互作用产生高次谐波的理论研究. 模拟发现, T型堆栈双层MoS2产生的高次谐波在高能区域的转换效率比AA型堆栈双层MoS2高一个数量级. 理论分析表明, 由于原子级错位堆栈下晶体对称性被打破, 使原有的部分带间禁戒跃迁路径被打开, 带间跃迁激发通道增加, 大大增大了载流子跃迁概率, 从而增强了高次谐波转换效率. 此外, 对谐波产率的波长定标研究表明, 在较长波长的激光驱动下 (> 2000 nm), T型堆栈下所增强的高次谐波具有更高的波长依赖. 该工作为如何优化增强固体高次谐波的转换效率提供一种新思路.
    In this paper, the high-order harmonic generation by the interaction between strong laser and bilayer MoS2 material is studied by numerically solving the multi-band semiconductor Bloch equations. It is found that the conversion efficiency of high-order harmonics generated by T-stacking bilayer MoS2 is one order of magnitude higher than that of AA-stacking bilayer MoS2. The theoretical analysis shows that due to the breaking of crystal symmetry under the atomic level dislocation, part of the interband forbidden transition paths are opened, and the excitation channels of interband transition are increased, which greatly increases the carrier transition probability and enhances the high-order harmonic conversion efficiency. In addition, the study of wavelength scaling of harmonic yield shows that the enhanced high-order harmonics in T-stacking bilayer are better wavelength-dependent under the action of a long wavelength laser (> 2000 nm). This work provides a new idea of how to optimize and enhance the conversion efficiency of solid-state high-order harmonics.
      通信作者: 余超, chaoyu@njust.edu.cn ; 陆瑞锋, rflu@njust.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11704187, 11974185, 11834004)、中央高校基本科研业务费专项资金(批准号: 30920021153)和中国博士后科学基金(批准号: 2019M661841)资助的课题
      Corresponding author: Yu Chao, chaoyu@njust.edu.cn ; Lu Rui-Feng, rflu@njust.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11704187, 11974185, 11834004), the Fundamental Research Funds for the Central Universities (Grant No. 30920021153), and the Project Funded by China Postdoctoral Science Foundation (Grant No. 2019M661841)
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    Ghimire S, Reis D A 2019 Nat. Phys. 15 10Google Scholar

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    Ghimire S, Dichiara A D, Sistrunk E, Agostini P, Dimauro L F, Reis D A 2011 Nat. Phys. 7 138Google Scholar

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    Ghimire S, Dichiara A D, Sistrunk E, Szafruga U B, Agostini P, Dimauro L F, Reis D A 2011 Phys. Rev. Lett. 107 167407Google Scholar

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    Zaks B, Liu R B, Sherwin M S 2012 Nature 483 580Google Scholar

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    Schubert O, Hohenleutner M, Langer F, Urbanek B, Lange C, Huttner U, Golde D, Meier T, Kira M, Koch S W 2014 Nat. Photonics 8 119Google Scholar

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    Luu T T, Garg M, Kruchinin S Y, Moulet A, Hassan M T, Goulielmakis E 2015 Nature 521 498Google Scholar

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    Vampa G, Hammond T J, Thire N, Schmidt B E, Legare F, Mcdonald C R, Brabec T, Corkum P B 2015 Nature 522 462Google Scholar

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    Vampa G, Hammond T J, Thire N, Schmidt B E, Legare F, Mcdonald C R, Brabec T, Klug D D, Corkum P B 2015 Phys. Rev. Lett. 115 193603Google Scholar

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    You Y S, Reis D A, Ghimire S 2017 Nat. Phys. 13 345Google Scholar

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    Korbman M, Kruchinin S Y, Yakovlev V S 2013 New J. Phys. 15 013006Google Scholar

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    Hawkins P G, Ivanov M Y, Yakovlev V S 2015 Phys. Rev. A 91 013405Google Scholar

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    Wu M, Ghimire S, Reis D A, Schafer K J, Gaarde M B 2015 Phys. Rev. A 91 043839Google Scholar

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    Guan Z, Zhou X X, Bian X B 2016 Phys. Rev. A 93 033852Google Scholar

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    Jin J Z, Xiao X R, Liang H, Wang M X, Chen S G, Gong Q, Peng L Y 2018 Phys. Rev. A 97 043420Google Scholar

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    Li L N, He F 2016 J. Opt. Soc. Am. B 34 2707

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    Li J, Zhang Q, Li L, Zhu X, Huang T, Lan P, Lu P 2019 Phys. Rev. A 99 033421Google Scholar

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    Vampa G, McDonald C R, Orlando G, Klug D D, Corkum P B, Brabec T 2014 Phys. Rev. Lett. 113 073901Google Scholar

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    McDonald C R, Vampa G, Corkum P B, Brabec T 2015 Phys. Rev. A 92 033845Google Scholar

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    Vampa G, McDonald C R, Orlando G, Corkum P B, Brabec T 2015 Phys. Rev. B 91 064302Google Scholar

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    Golde D, Meier T, Koch S W 2006 J. Opt. Soc. Am. B 23 2559Google Scholar

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    Golde D, Meier T, Koch S W 2008 Phys.Rev. B 77 075330Google Scholar

    [25]

    Golde D, Kira M, Meier T, Koch S W 2011 Phys. Status Solidi B 248 863Google Scholar

    [26]

    Földi P, Benedict M G, Yakovlev V S 2013 New J. Phys. 15 063019Google Scholar

    [27]

    Tamaya T, Ishikawa A, Ogawa T, Tanaka K 2016 Phys. Rev. Lett. 116 016601Google Scholar

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    Hohenleutner M, Langer F, Schubert O, Knorr M, Huttner U, Koch S W, Kira M, Huber R 2015 Nature 523 572Google Scholar

    [29]

    Yu C, Jiang S C, Wu T, Yuan G L, Peng Y G, Jin C, Lu R F 2020 Phys. Rev. B 102 241407(RGoogle Scholar

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    Li J B, Xiao Z, Yue S J, Wu H M, Du H C 2017 Opt. Express 25 18603Google Scholar

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    Liu H, Guo C, Giulio V, Zhang J L, Tomas S, Meng X, Bucksbaum P H, Jelena V, Fan S, Reis D A 2018 Nat. Phys. 14 1006Google Scholar

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    Franz D, Kaassamani S, Gauthier D, Nicolas R, K Holodtsova M, Douillard L, Gomes J T, Lavoute L, Gaponov D, Ducros N 2019 Sci. Rep. 9 5663Google Scholar

    [33]

    Yu C, Jiang S C, Wu T, Yuan G L, Wang Z W, Jin C, Lu R F 2018 Phys. Rev. B 98 085439Google Scholar

    [34]

    Liu H, Li Y, You Y S, Ghimire S, Heinz T F, Reis D A 2017 Nat. Phys. 13 262Google Scholar

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    Tate J, Auguste T, Muller H G, Salières P, Agostini P, DiMauro L F 2007 Phys. Rev. Lett. 98 013901Google Scholar

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    Schiessl K, Ishikava K L, Persson E, Burgdörfer J 2007 Phys. Rev. Lett. 99 253903Google Scholar

  • 图 1  (a)和(b)分别为双层MoS2材料AA型堆栈和T型堆栈结构的俯视图(上图)和侧视图(下图); (c) 双层MoS2材料的第一布里渊区; (d)和(e) 分别为双层MoS2材料AA型堆栈和T型堆栈在高对称性Γ–M方向的能带结构

    Fig. 1.  Top and side views of bilayer MoS2 for (a) AA stacking and (b) T stacking; (c) the first brillouin zone of bilayer MoS2; (d) energy bands of bilayer MoS2 for (a) AA stacking and (b) T stacking in Γ–M direction.

    图 2  模拟计算得到的双层MoS2材料在高对称性ΓM方向的高次谐波谱(红线为T型堆栈, 蓝线为AA型堆栈) (a) 模拟过程中使用12条价带8条导带; (b) 模拟过程中使用2条价带4条导带; (c) 模拟过程中使用4条价带4条导带

    Fig. 2.  Calculated high harmonic spectra from bilayer MoS2 in AA stacking (blue line) and T stacking(red line) with (a) twelve valence bands and eight conduction bands; (b) two valence bands and four conduction bands; (c) four valence bands and four conduction bands used in simulation.

    图 3  双层MoS2材料的部分带间跃迁偶极矩 (a)和(b)分别为AA型堆栈的双层MoS2材料中第三条价带v3和第四条价带v4与最低4条导带的带间跃迁偶极矩; (c)和(d)分别为T型堆栈的双层MoS2材料中第三条价带v3和第四条价带v4与最低4条导带的带间跃迁偶极矩

    Fig. 3.  The parts of transition dipole moments: (a) and (b) show the transition dipole moments among two valence bands (v3 and v4) and four lowest conduction bands in AA stacking, respectively; (c) and (d) how the transition dipole moments among two valence bands (v3 and v4) and four lowest conduction bands in T stacking, respectively.

    图 4  模拟计算得到的双层MoS2材料随驱动激光波长变化的高次谐波谱 (a) AA型堆栈; (b) T型堆栈

    Fig. 4.  Wavelength dependent high harmonic spectra from bilayer MoS2 in (a) AA stacking and (b) T stacking.

    图 5  模拟得到的双层MoS2材料高次谐波产率的波长定标 (a) AA型堆栈; (b) T型堆栈; 图中直线由波长定标公式拟合得到

    Fig. 5.  Wavelength scaling of high harmonic yield from bilayer MoS2 in (a) AA stacking and (b) T stacking. Lines are fits of the scaling law to the data.

  • [1]

    Huttner U, Kira M, and Koch S W 2017 Laser Photon. Rev. 11 1700049Google Scholar

    [2]

    Kruchinin S Y, Krausz F, Yakovlev V S 2018 Rev. Mod. Phys. 90 021002Google Scholar

    [3]

    Ghimire S, Reis D A 2019 Nat. Phys. 15 10Google Scholar

    [4]

    Yu C, Jiang S C, Lu R F 2019 Adv. Phys. X 4 1562982

    [5]

    Ghimire S, Dichiara A D, Sistrunk E, Agostini P, Dimauro L F, Reis D A 2011 Nat. Phys. 7 138Google Scholar

    [6]

    Ghimire S, Dichiara A D, Sistrunk E, Szafruga U B, Agostini P, Dimauro L F, Reis D A 2011 Phys. Rev. Lett. 107 167407Google Scholar

    [7]

    Zaks B, Liu R B, Sherwin M S 2012 Nature 483 580Google Scholar

    [8]

    Schubert O, Hohenleutner M, Langer F, Urbanek B, Lange C, Huttner U, Golde D, Meier T, Kira M, Koch S W 2014 Nat. Photonics 8 119Google Scholar

    [9]

    Luu T T, Garg M, Kruchinin S Y, Moulet A, Hassan M T, Goulielmakis E 2015 Nature 521 498Google Scholar

    [10]

    Vampa G, Hammond T J, Thire N, Schmidt B E, Legare F, Mcdonald C R, Brabec T, Corkum P B 2015 Nature 522 462Google Scholar

    [11]

    Vampa G, Hammond T J, Thire N, Schmidt B E, Legare F, Mcdonald C R, Brabec T, Klug D D, Corkum P B 2015 Phys. Rev. Lett. 115 193603Google Scholar

    [12]

    You Y S, Reis D A, Ghimire S 2017 Nat. Phys. 13 345Google Scholar

    [13]

    Korbman M, Kruchinin S Y, Yakovlev V S 2013 New J. Phys. 15 013006Google Scholar

    [14]

    Hawkins P G, Ivanov M Y, Yakovlev V S 2015 Phys. Rev. A 91 013405Google Scholar

    [15]

    Wu M, Ghimire S, Reis D A, Schafer K J, Gaarde M B 2015 Phys. Rev. A 91 043839Google Scholar

    [16]

    Guan Z, Zhou X X, Bian X B 2016 Phys. Rev. A 93 033852Google Scholar

    [17]

    Jin J Z, Xiao X R, Liang H, Wang M X, Chen S G, Gong Q, Peng L Y 2018 Phys. Rev. A 97 043420Google Scholar

    [18]

    Li L N, He F 2016 J. Opt. Soc. Am. B 34 2707

    [19]

    Li J, Zhang Q, Li L, Zhu X, Huang T, Lan P, Lu P 2019 Phys. Rev. A 99 033421Google Scholar

    [20]

    Vampa G, McDonald C R, Orlando G, Klug D D, Corkum P B, Brabec T 2014 Phys. Rev. Lett. 113 073901Google Scholar

    [21]

    McDonald C R, Vampa G, Corkum P B, Brabec T 2015 Phys. Rev. A 92 033845Google Scholar

    [22]

    Vampa G, McDonald C R, Orlando G, Corkum P B, Brabec T 2015 Phys. Rev. B 91 064302Google Scholar

    [23]

    Golde D, Meier T, Koch S W 2006 J. Opt. Soc. Am. B 23 2559Google Scholar

    [24]

    Golde D, Meier T, Koch S W 2008 Phys.Rev. B 77 075330Google Scholar

    [25]

    Golde D, Kira M, Meier T, Koch S W 2011 Phys. Status Solidi B 248 863Google Scholar

    [26]

    Földi P, Benedict M G, Yakovlev V S 2013 New J. Phys. 15 063019Google Scholar

    [27]

    Tamaya T, Ishikawa A, Ogawa T, Tanaka K 2016 Phys. Rev. Lett. 116 016601Google Scholar

    [28]

    Hohenleutner M, Langer F, Schubert O, Knorr M, Huttner U, Koch S W, Kira M, Huber R 2015 Nature 523 572Google Scholar

    [29]

    Yu C, Jiang S C, Wu T, Yuan G L, Peng Y G, Jin C, Lu R F 2020 Phys. Rev. B 102 241407(RGoogle Scholar

    [30]

    Li J B, Xiao Z, Yue S J, Wu H M, Du H C 2017 Opt. Express 25 18603Google Scholar

    [31]

    Liu H, Guo C, Giulio V, Zhang J L, Tomas S, Meng X, Bucksbaum P H, Jelena V, Fan S, Reis D A 2018 Nat. Phys. 14 1006Google Scholar

    [32]

    Franz D, Kaassamani S, Gauthier D, Nicolas R, K Holodtsova M, Douillard L, Gomes J T, Lavoute L, Gaponov D, Ducros N 2019 Sci. Rep. 9 5663Google Scholar

    [33]

    Yu C, Jiang S C, Wu T, Yuan G L, Wang Z W, Jin C, Lu R F 2018 Phys. Rev. B 98 085439Google Scholar

    [34]

    Liu H, Li Y, You Y S, Ghimire S, Heinz T F, Reis D A 2017 Nat. Phys. 13 262Google Scholar

    [35]

    Tate J, Auguste T, Muller H G, Salières P, Agostini P, DiMauro L F 2007 Phys. Rev. Lett. 98 013901Google Scholar

    [36]

    Schiessl K, Ishikava K L, Persson E, Burgdörfer J 2007 Phys. Rev. Lett. 99 253903Google Scholar

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出版历程
  • 收稿日期:  2021-04-18
  • 修回日期:  2021-05-22
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-07-05

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