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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.
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Keywords:
- high harmonic generation /
- bilayer MoS2 /
- stacking pattern /
- wavelength scaling
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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Γ–M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.
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[1] Huttner U, Kira M, and Koch S W 2017 Laser Photon. Rev. 11 1700049
Google Scholar
[2] Kruchinin S Y, Krausz F, Yakovlev V S 2018 Rev. Mod. Phys. 90 021002
Google Scholar
[3] Ghimire S, Reis D A 2019 Nat. Phys. 15 10
Google 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. 7 138
Google 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 167407
Google Scholar
[7] Zaks B, Liu R B, Sherwin M S 2012 Nature 483 580
Google 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 8 119
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[9] Luu T T, Garg M, Kruchinin S Y, Moulet A, Hassan M T, Goulielmakis E 2015 Nature 521 498
Google Scholar
[10] Vampa G, Hammond T J, Thire N, Schmidt B E, Legare F, Mcdonald C R, Brabec T, Corkum P B 2015 Nature 522 462
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[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 193603
Google Scholar
[12] You Y S, Reis D A, Ghimire S 2017 Nat. Phys. 13 345
Google Scholar
[13] Korbman M, Kruchinin S Y, Yakovlev V S 2013 New J. Phys. 15 013006
Google Scholar
[14] Hawkins P G, Ivanov M Y, Yakovlev V S 2015 Phys. Rev. A 91 013405
Google Scholar
[15] Wu M, Ghimire S, Reis D A, Schafer K J, Gaarde M B 2015 Phys. Rev. A 91 043839
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Google 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 043420
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Google Scholar
[21] McDonald C R, Vampa G, Corkum P B, Brabec T 2015 Phys. Rev. A 92 033845
Google Scholar
[22] Vampa G, McDonald C R, Orlando G, Corkum P B, Brabec T 2015 Phys. Rev. B 91 064302
Google Scholar
[23] Golde D, Meier T, Koch S W 2006 J. Opt. Soc. Am. B 23 2559
Google Scholar
[24] Golde D, Meier T, Koch S W 2008 Phys.Rev. B 77 075330
Google Scholar
[25] Golde D, Kira M, Meier T, Koch S W 2011 Phys. Status Solidi B 248 863
Google Scholar
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Google Scholar
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Google Scholar
[28] Hohenleutner M, Langer F, Schubert O, Knorr M, Huttner U, Koch S W, Kira M, Huber R 2015 Nature 523 572
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[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(R
Google Scholar
[30] Li J B, Xiao Z, Yue S J, Wu H M, Du H C 2017 Opt. Express 25 18603
Google Scholar
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Google 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 5663
Google 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 085439
Google Scholar
[34] Liu H, Li Y, You Y S, Ghimire S, Heinz T F, Reis D A 2017 Nat. Phys. 13 262
Google Scholar
[35] Tate J, Auguste T, Muller H G, Salières P, Agostini P, DiMauro L F 2007 Phys. Rev. Lett. 98 013901
Google Scholar
[36] Schiessl K, Ishikava K L, Persson E, Burgdörfer J 2007 Phys. Rev. Lett. 99 253903
Google Scholar
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