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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
Figure 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
Figure 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
Figure 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
Figure 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
Figure 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.
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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
Google Scholar
[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
Google 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 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
Google Scholar
[16] Guan Z, Zhou X X, Bian X B 2016 Phys. Rev. A 93 033852
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
Google 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 033421
Google Scholar
[20] Vampa G, McDonald C R, Orlando G, Klug D D, Corkum P B, Brabec T 2014 Phys. Rev. Lett. 113 073901
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
[26] Földi P, Benedict M G, Yakovlev V S 2013 New J. Phys. 15 063019
Google Scholar
[27] Tamaya T, Ishikawa A, Ogawa T, Tanaka K 2016 Phys. Rev. Lett. 116 016601
Google Scholar
[28] Hohenleutner M, Langer F, Schubert O, Knorr M, Huttner U, Koch S W, Kira M, Huber R 2015 Nature 523 572
Google 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(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
[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 1006
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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