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Excitation energy transfer is one of the most important factors affecting the applications of para-sexiphenyl devices. The study of exciton dynamics and exciton coherence effect of para-sexiphenyl clusters under external field excitation is important in order to improve the performance of molecular devices composed of para-sexiphenyl and its related derivatives. In this work, the two-dimensional disc-like para-sexiphenyl molecular cluster is used as the object of study. The molecular system is simplified into a two-level model based on its structural features and energy level distribution. Within the framework of density matrix theory, the exciton dynamics and exciton coherence behavior of disk-like para-hexaphene molecular clusters excited by different pulse fields are analyzed through using the mathematical mean value approximation of the operator. The results show that when long pulses are used to excite para-sexiphenyl clusters, the single exciton state characteristic appears and is insensitive to the change of excited external field strength. When the clusters are subjected to strong pulsed fields with short pulse widths, multiple excitons are excited simultaneously in the cluster, forming multiple exciton states, with the exciton energy levels shifting toward lower energy and new hybrid states appearing. In the optical response spectrum, there appear multiple resonance peaks. And as the pulse field is enhanced, the multi-exciton effect becomes apparent and the hybridization energy level increases. Under short pulse excitation, the excited states are distributed differently in different energy regions, but all of them show obvious symmetry. As the highest-energy exciton states of H-type clusters are preferentially excited, we analyze the exciton state population and the exciton coherence evolution with time in the high-energy exciton state. With the pulse field increases, Rabi oscillations appear and the exciton coherence effect increases. When the pulsed field reaches a certain field strength, the exciton oscillation cooperativity disappears in the first 100 fs, showing the non-local characteristic. The position of the wave trough of the exciton state population corresponds to the peak in the exciton coherence size. It indicates that when the pulse field is intense enough, a large number of molecules are in the exciton coherent state during the pulsed excitation, and transient out-of-domain phenomena occur.
[1] O’ Carroll D M, Petoukhoff C E, Kohl J, Yu B X, Carter C M, Goodman S 2013 Polym. Chem. 4 5181
Google Scholar
[2] Reineke S, Thomschke M, Lussem B, Leo K 2013 Rev. Mod. Phys. 85 1245
Google Scholar
[3] Zhang C X, Liu R G, Mak C H, Zou X L, Shen H H, Leu S Y, Ji L, Hsu H Y 2018 J. Photonics Energy 8 021001
Google Scholar
[4] Spano F C, Silva C 2014 Annu. Rev. Phys. Chem. 65 477
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[5] Brixner T, Hildner R, Kohler J, Lambert C, Wurthner F 2017 Adv. Energy Mater. 7 1700236
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[6] Tamai Y, Ohkita H, Benten H, Ito S 2015 J. Phys. Chem. Lett. 6 3417
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[7] Resel R 2003 Thin Solid Films 433 1
Google Scholar
[8] Zojer E, Koch N, Puschnig P, Meghdadi F, Niko A, Resel R, Ambrosch-Draxl C, Knupfer M, Fink J, Bredas J L, Leising G 2000 Phys. Rev. B 61 16538
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[9] Palczynski K, Heimel G, Heyda J, Dzubiella J 2014 Cryst. Growth Des. 14 3791
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[10] Choi A, Kwon Y N, Chung J W, Yun Y, Park J I, Lee Y U 2020 AIP Adv. 10 025127
Google Scholar
[11] Zhang Y, Wei X C, Zhang H, Chen X, Wang J 2018 Appl. Surf. Sci. 427 452
Google Scholar
[12] Li Y, Wang H, Zhang X H, Zhang Q, Wang X S, Cao D F, Shi Z S, Yan D H, Cui Z C 2016 RSC Adv. 6 5377
Google Scholar
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Google Scholar
[14] Yang X X, Feng X, Xin J H, Zhang P L, Wang H B, Yan D H 2018 J. Mater. Chem. C 6 8879
Google Scholar
[15] Usluer O, Demic S , Kus M, Ozel F, Sariciftci N S 2014 J. Lumines. 146 6
Google Scholar
[16] Simbrunner C, Hernandez-Sosa G, Baumgartner E, Hesser G, Roither J, Heiss W, Sitter H 2009 Appl. Phys. Lett. 94 073505
Google Scholar
[17] Jiang X X, Dai J G, Wang H B, Geng Y H, Yan D H 2007 Chem. Phys. Lett. 446 329
Google Scholar
[18] Winder C, Andreev A, Sitter H, Matt G, Sariciftci N S, Meissner D 2003 Synth. Met. 139 573
Google Scholar
[19] Qian C, Sun J, Kong L A, Gou G Y, Zhu M L, Yuan Y B, Huang H, Gao Y L, Yang J L 2017 Adv. Funct. Mater. 27 1604933
Google Scholar
[20] Simbrunner C 2013 Semicond. Sci. Technol. 28 053001
Google Scholar
[21] Wang L, Plehn T, May V 2020 Phys. Rev. B 102 075401
Google Scholar
[22] Lee J, Zhang Q, Park S, Choe A, Fan Z, Ko H 2016 ACS Appl. Mater. Interfaces 8 634
Google Scholar
[23] Li G C, Zhang Q, Maier S A, Lei D 2018 Nanophotonics 7 1865
Google Scholar
[24] Fernandes J D, Pazin W M, Aroca R F, Macedo W D J, Teixeira S R, Constantino C J L 2019 Spectroc. Acta A 211 221
Google Scholar
[25] Zhang Y, Meng Q S, Zhang L, Luo Y, Yu Y J, Yang B, Zhang Y, Esteban R, Aizpurua J, Luo Y, Yang J L, Dong Z C, Hou J G 2017 Nat. Commun. 8 15225
Google Scholar
[26] Han X B, Li F, He Z C, Liu Y H, Hu H T, Wang K, Lu P X 2022 Nanophotonics 11 603
Google Scholar
[27] Kramer S N, Brown J, Rice M, Peteanu L A 2021 J. Phys. Chem. Lett. 12 5919
Google Scholar
[28] Wang L, May V 2016 Phys. Rev. B 94 195413
Google Scholar
[29] Wang L, May V 2018 J. Phys. B 51 064002
Google Scholar
[30] Kasha M 1963 Radiat. Res. 20 55
Google Scholar
[31] Chakraborty S, Debnath P, Dey D, Bhattacharjee D, Hussain S A 2014 J. Photochem. Photobiol. A Chem. 293 57
Google Scholar
[32] Wu F P, Lu Y X, Mu X L E, Chen Z T, Liu S S, Zhou X F, Liu S F, Li Z B 2020 ACS Appl. Mater. Interfaces 12 32388
Google Scholar
[33] Zhao X J, Zhao H J, Wang S, Fan Z W, Ma Y, Yin Y M, Wang W, Xi R M, Meng M 2021 J. Am. Chem. Soc. 143 20828
Google Scholar
[34] Gomez-Sosa G, Beristain M F, Ortega A, Martínez-Viramontes J, Ogawa T, Fernández-Hernández R C, Tamayo-Rivera L, Reyes-Esqueda J A, Isoshima T, Hara M 2012 Opt. Mater. 34 856
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Google Scholar
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Google Scholar
[37] May V 2014 J. Chem. Phys. 140 054103
Google Scholar
[38] Hader K, Consani C, Brixner T, Engel V 2017 Phys. Chem. Chem. Phys. 19 31989
Google Scholar
[39] Zheng F L, Chen L P, Gao J B, Zhao Y 2021 Materials 14 3291
Google Scholar
[40] Fassioli F, Dinshaw R, Arpin P C, Scholes G D 2014 J. R. Soc. Interface 11 20130901
Google Scholar
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图 1 二维对六苯团簇结构图 (a) 俯视图; (b) 沿x轴侧视图; (c) 沿y轴侧视图
Figure 1. Structure of the two-dimensional 6P clusters: (a) Top view; (b) side view along x axis; (c) side view along y axis.
图 2 二维对六苯团簇静电位移示意图 (a) 分子激发能的相对静电位移; (b) 分子激发能无(红色)及有(蓝色)静电位移时的Frenkel激子能带[21]
Figure 2. Schematic diagram of the electrostatic displacement of two-dimensional 6P clusters: (a) Relative electrostatic shift of the molecular excitation energies; (b) Frenkel exciton energy band without (red) and with (blue) electrostatic shift of the molecular excitation energies[21].
图 3
$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ 时, 团簇内激发态布居$ P_{{\text{tot}}}^{\left( {{\text{ss}}} \right)} $ 随激光$\hbar {\omega _0}$ 、脉冲宽度${\tau _{\text{p}}}$ 变化 (a) 弱场${a_{\text{p}}}=5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (b) 强场${a_{\text{p}}}{\text{ = 2}}.5 \times {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ Figure 3. Excited-state populations
$ P_{{\text{tot}}}^{\left( {{\text{ss}}} \right)} $ in clusters vary with photon energy$\hbar {\omega _0}$ of the laser and pulse length${\tau _{\text{p}}}$ at$\kappa = 2 \;\times $ $ {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ : (a) In weak fields${a_{\text{p}}}=5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (b) in strong fields$ a_{\text{p}}\text{ = 2}.5\times10^{6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}} $ .
图 4
$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ 时, 在长脉冲场 (a)${\tau _{\text{p}}}=1{\text{ ps}}$ 和短脉冲场(b)${\tau _{\text{p}}}=50{\text{ fs}}$ 下, 团簇内激发态布居$ P_{{\text{tot}}}^{\left( {{\text{ss}}} \right)} $ 随激光$\hbar {\omega _0}$ 、脉冲能量${a_{\text{p}}}$ 变化Figure 4. Excited-state populations
$ P_{{\text{tot}}}^{\left( {{\text{ss}}} \right)} $ in clusters in long${\tau _{\text{p}}}=1{\text{ ps}}$ (a) and short${\tau _{\text{p}}}=50{\text{ fs}}$ (b) pulsed fields vary with photon energy$\hbar {\omega _0}$ of the laser and pulse energy${a_{\text{p}}}$ ,$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ .
图 5
$\hbar {\omega _0} = 4.2483{\text{ eV}}$ ,$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ 时, 弱场短脉冲作用下(${a_{\text{p}}} = 5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ,${\tau _{\text{p}}} = 50~{\text{fs}}$ ), 4个不同时刻的分子激发态布居$ {P_m} $ (a)$t = 100{\text{ fs}}$ ; (b)$t = 200{\text{ fs}}$ ; (c)$t = 500{\text{ fs}}$ ; (d)$t = 1{\text{ ps}}$ Figure 5. Molecular excited state populations
$ {P_m} $ at four different moments in the weak field with short pulses (${a_{\text{p}}} = $ $ 5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ,${\tau _{\text{p}}} = 50{\text{ fs}}$ ),$\hbar {\omega _0} = 4.2483{\text{ eV}}$ ,$\kappa = 2 \times $ $ {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ : (a)$t = 100{\text{ fs}}$ ; (b)$t = 200{\text{ fs}}$ ; (c)$t = 500{\text{ fs}}$ ; (d)$t = 1{\text{ ps}}$ .
图 6
$\hbar {\omega _0} = 4.9243{\text{ eV}}$ ,$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ 时, 弱场短脉冲作用下(${a_{\text{p}}} = 5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ,${\tau _{\text{p}}}{=}50{\text{ fs}}$ ), 4个不同时刻的分子激发态布居$ {P_m} $ (a)$t = 100{\text{ fs}}$ ; (b)$t = 200{\text{ fs}}$ ; (c)$t = 500{\text{ fs}}$ ; (d)$t = 1{\text{ ps}}$ Figure 6. Molecular excited state populations
$ {P_m} $ at four different moments in the weak field with short pulses (${a_{\text{p}}} = $ $ 5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ,${\tau _{\text{p}}}{=}50{\text{ fs}}$ ),$\hbar {\omega _0} = 4.9243{\text{ eV}}$ ,$\kappa = 2 \times $ $ {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ : (a)$t = 100{\text{ fs}}$ ; (b)$t = 200{\text{ fs}}$ ; (c)$t = 500{\text{ fs}}$ ; (d)$t = 1{\text{ ps}}$ .
图 7 二维对六苯团簇选取分子示意图
Figure 7. Schematic diagram of selected molecules in two-dimensional 6P clusters clusters.
图 8
$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ 时, 短脉冲(${\tau _{\text{p}}} = 50{\text{ fs}}$ ,$\hbar {\omega _0} = 4.9243{\text{ eV}}$ )场下, 分子激发态布居$ {P_m} $ 随时间的演变 (a)${a_{\text{p}}} = 5 \times $ $ {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (b)$ {a_{\text{p}}} = {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}} $ ; (c)${a_{\text{p}}} = 2.5 \times {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (d)${a_{\text{p}}} = 5 \times {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ Figure 8. Molecular excited state populations
$ {P_m} $ in short pulsed fields (${\tau _{\text{p}}} = 50{\text{ fs}}$ ,$\hbar {\omega _0} = 4.9243{\text{ eV}}$ ) vary with time,$\kappa = 2 \times $ $ {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ : (a)${a_{\text{p}}} = 5 \times {10^5}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (b)$ {a_{\text{p}}} = {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (c)${a_{\text{p}}} = 2.5 \times {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ ; (d)${a_{\text{p}}} = 5 \times {10^6}{\text{ ps}} {\cdot} {\rm{V{\cdot}m^{-1}}}$ .
图 9 在
$\kappa = 2 \times {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ , 短脉冲(${\tau _{\text{p}}} = 50{\text{ fs}}$ ,$\hbar {\omega _0} = $ $ 4.9243{\text{ eV}}$ )场下, 激子相干尺寸$ {L_\rho } $ 随时间的演变Figure 9. Exciton coherence size
$ {L_\rho } $ in short pulsed fields (${\tau _{\text{p}}} = $ $ 50{\text{ fs}}$ ,$\hbar {\omega _0} = 4.9243{\text{ eV}}$ ) vary with time at$\kappa = 2 \times $ $ {10^{11}}{\text{ }}{{\text{s}}^{{{ - 1}}}}$ .表 1 参数设置
Table 1. Parameters used.
名称/单位 数值 分子数${N_{{\text{mol}}}}$ 59 分子本征态能量$ {E_{{\text{mol}}}} $/eV 4.02 分子偶极矩$ {d_{{\text{mol}}}} $/D 12.4 分子间激发能量转移速率$\kappa $/(1011 s–1) 2 脉冲场频率${\omega _0}$ 随${E_0}/\hbar $变化 脉冲场强度${E_0}$/(V·m–1) 105—108 脉冲宽度${\tau _{\text{p}}}$/fs 20—1000 
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[1] O’ Carroll D M, Petoukhoff C E, Kohl J, Yu B X, Carter C M, Goodman S 2013 Polym. Chem. 4 5181
Google Scholar
[2] Reineke S, Thomschke M, Lussem B, Leo K 2013 Rev. Mod. Phys. 85 1245
Google Scholar
[3] Zhang C X, Liu R G, Mak C H, Zou X L, Shen H H, Leu S Y, Ji L, Hsu H Y 2018 J. Photonics Energy 8 021001
Google Scholar
[4] Spano F C, Silva C 2014 Annu. Rev. Phys. Chem. 65 477
Google Scholar
[5] Brixner T, Hildner R, Kohler J, Lambert C, Wurthner F 2017 Adv. Energy Mater. 7 1700236
Google Scholar
[6] Tamai Y, Ohkita H, Benten H, Ito S 2015 J. Phys. Chem. Lett. 6 3417
Google Scholar
[7] Resel R 2003 Thin Solid Films 433 1
Google Scholar
[8] Zojer E, Koch N, Puschnig P, Meghdadi F, Niko A, Resel R, Ambrosch-Draxl C, Knupfer M, Fink J, Bredas J L, Leising G 2000 Phys. Rev. B 61 16538
Google Scholar
[9] Palczynski K, Heimel G, Heyda J, Dzubiella J 2014 Cryst. Growth Des. 14 3791
Google Scholar
[10] Choi A, Kwon Y N, Chung J W, Yun Y, Park J I, Lee Y U 2020 AIP Adv. 10 025127
Google Scholar
[11] Zhang Y, Wei X C, Zhang H, Chen X, Wang J 2018 Appl. Surf. Sci. 427 452
Google Scholar
[12] Li Y, Wang H, Zhang X H, Zhang Q, Wang X S, Cao D F, Shi Z S, Yan D H, Cui Z C 2016 RSC Adv. 6 5377
Google Scholar
[13] Katiyar S, Verma N, Jogi J 2022 Semicond. Sci. Technol. 37 025008
Google Scholar
[14] Yang X X, Feng X, Xin J H, Zhang P L, Wang H B, Yan D H 2018 J. Mater. Chem. C 6 8879
Google Scholar
[15] Usluer O, Demic S , Kus M, Ozel F, Sariciftci N S 2014 J. Lumines. 146 6
Google Scholar
[16] Simbrunner C, Hernandez-Sosa G, Baumgartner E, Hesser G, Roither J, Heiss W, Sitter H 2009 Appl. Phys. Lett. 94 073505
Google Scholar
[17] Jiang X X, Dai J G, Wang H B, Geng Y H, Yan D H 2007 Chem. Phys. Lett. 446 329
Google Scholar
[18] Winder C, Andreev A, Sitter H, Matt G, Sariciftci N S, Meissner D 2003 Synth. Met. 139 573
Google Scholar
[19] Qian C, Sun J, Kong L A, Gou G Y, Zhu M L, Yuan Y B, Huang H, Gao Y L, Yang J L 2017 Adv. Funct. Mater. 27 1604933
Google Scholar
[20] Simbrunner C 2013 Semicond. Sci. Technol. 28 053001
Google Scholar
[21] Wang L, Plehn T, May V 2020 Phys. Rev. B 102 075401
Google Scholar
[22] Lee J, Zhang Q, Park S, Choe A, Fan Z, Ko H 2016 ACS Appl. Mater. Interfaces 8 634
Google Scholar
[23] Li G C, Zhang Q, Maier S A, Lei D 2018 Nanophotonics 7 1865
Google Scholar
[24] Fernandes J D, Pazin W M, Aroca R F, Macedo W D J, Teixeira S R, Constantino C J L 2019 Spectroc. Acta A 211 221
Google Scholar
[25] Zhang Y, Meng Q S, Zhang L, Luo Y, Yu Y J, Yang B, Zhang Y, Esteban R, Aizpurua J, Luo Y, Yang J L, Dong Z C, Hou J G 2017 Nat. Commun. 8 15225
Google Scholar
[26] Han X B, Li F, He Z C, Liu Y H, Hu H T, Wang K, Lu P X 2022 Nanophotonics 11 603
Google Scholar
[27] Kramer S N, Brown J, Rice M, Peteanu L A 2021 J. Phys. Chem. Lett. 12 5919
Google Scholar
[28] Wang L, May V 2016 Phys. Rev. B 94 195413
Google Scholar
[29] Wang L, May V 2018 J. Phys. B 51 064002
Google Scholar
[30] Kasha M 1963 Radiat. Res. 20 55
Google Scholar
[31] Chakraborty S, Debnath P, Dey D, Bhattacharjee D, Hussain S A 2014 J. Photochem. Photobiol. A Chem. 293 57
Google Scholar
[32] Wu F P, Lu Y X, Mu X L E, Chen Z T, Liu S S, Zhou X F, Liu S F, Li Z B 2020 ACS Appl. Mater. Interfaces 12 32388
Google Scholar
[33] Zhao X J, Zhao H J, Wang S, Fan Z W, Ma Y, Yin Y M, Wang W, Xi R M, Meng M 2021 J. Am. Chem. Soc. 143 20828
Google Scholar
[34] Gomez-Sosa G, Beristain M F, Ortega A, Martínez-Viramontes J, Ogawa T, Fernández-Hernández R C, Tamayo-Rivera L, Reyes-Esqueda J A, Isoshima T, Hara M 2012 Opt. Mater. 34 856
Google Scholar
[35] Plehn T, Ziemann D, May V 2018 Phys. Chem. Chem. Phys. 20 26870
Google Scholar
[36] Plehn T, Ziemann D, May V 2019 J. Phys. Chem. C 122 27925
Google Scholar
[37] May V 2014 J. Chem. Phys. 140 054103
Google Scholar
[38] Hader K, Consani C, Brixner T, Engel V 2017 Phys. Chem. Chem. Phys. 19 31989
Google Scholar
[39] Zheng F L, Chen L P, Gao J B, Zhao Y 2021 Materials 14 3291
Google Scholar
[40] Fassioli F, Dinshaw R, Arpin P C, Scholes G D 2014 J. R. Soc. Interface 11 20130901
Google Scholar
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