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By using non-equilibrium Green’s function method, we investigate the thermoelectric properties of molecular junctions based on acene-linked graphene nanoribbons. The effects of the length of the acene molecule, the contact position between the acene molecule and graphene nanoribbon electrode on the thermoelectric parameters are mainly considered in this work. It is found that the phonon contribution is dominant in the thermal conductance corresponding to the maximum of the thermoelectric figure of merit (ZTmax). As the length of the acene molecule increases, the phonon thermal conductance decreases monotonically, and eventually becomes almost independent of the acene molecule’ length. When the acene molecules contact the middle (upper) part of the left (right) electrode of graphene nanoribbon, the corresponding ZTmax is the highest. However, when the acene molecules contact the middle (middle) part of the left (right) electrode of graphene nanoribbons, the corresponding ZTmax is the lowest. As the temperature increases, ZTmax has a monotonically increasing tendency, regardless of the contact position. With the increase of the length of the acene molecule, the chemical potential corresponding to ZTmax becomes closer to the intrinsic Fermi level. The above findings may provide the valuable reference for the future design of thermoelectric devices based on the acene molecular junctions.
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Keywords:
- thermal transport /
- electronic transmission /
- thermoelectric properties /
- acene molecular junctions
[1] Wu C W, Ren X, Xie G, Zhou W X, Zhang G, Chen K Q 2022 Phys. Rev. Appl. 18 014053Google Scholar
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[3] Li N, Ren J, Wang L, Zhang G, Hanggi P, Li B 2012 Rev. Mod. Phys. 84 1045Google Scholar
[4] Su L, Wang D, Wang S, Qin B, Wang Y, Qin Y, Jin Y, Chang C, Zhao L D 2022 Science 375 1385Google Scholar
[5] 陈晓彬, 段文晖 2015 物理学报 64 186302Google Scholar
Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302Google Scholar
[6] Jia P Z, Xie Z X, Deng Y X, Zhang Y, Tang L M, Zhou W X, Chen K Q 2022 Appl. Phys. Lett. 121 043901Google Scholar
[7] 余泽浩, 张力发, 吴靖, 赵云山 2023 物理学报 72 057301Google Scholar
Yu Z H, Zhang L F, Wu J, Zhao Y S 2023 Acta Phys. Sin. 72 057301Google Scholar
[8] Shi X L, Zou J, Chen Z G 2020 Chem. Rev. 120 7399Google Scholar
[9] Wang T, Zhang C, Snoussi H, Zhang G 2020 Adv. Funct. Mater. 30 1906041Google Scholar
[10] Xie Q Y, Ma J J, Liu Q Y, Liu P F, Zhang P, Zhang K W, Wang B T 2022 Phys. Chem. Chem. Phys. 24 7303Google Scholar
[11] Zhou Z Z, Liu H J, Fan D D, Cao G H, Sheng C Y 2019 Phys. Rev. B 99 085410Google Scholar
[12] Deng L, Chen G M 2021 Nano Energy 80 105448Google Scholar
[13] Xie Z X, Tang L M, Pan C N, Li K M, Chen K Q, Duan W 2012 Appl. Phys. Lett. 100 073105Google Scholar
[14] Ouyang Y, Guo J 2009 Appl. Phys. Lett. 94 263107Google Scholar
[15] 王艳, 陈南迪, 杨陈, 曾召益, 胡翠娥, 陈向荣 2021 物理学报 70 116301Google Scholar
Wang Y, Chen N D, Chen Y, Zeng Z Y, Hu C E, Chen X R 2021 Acta Phys. Sin. 70 116301Google Scholar
[16] Jiang J W, Wang J S, Li B 2011 J. Appl. Phys. 109 014326Google Scholar
[17] Pan H, Tang L M, Chen K Q 2022 Phys. Rev. B 105 064401Google Scholar
[18] Pan H, Ding Z K, Zeng B W, Luo N N, Zeng J, Tang L M, Chen K Q 2023 Phys. Rev. B 107 104303Google Scholar
[19] Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727Google Scholar
[20] 宗志成, 潘东楷, 邓世琛, 万骁, 杨哩娜, 马登科, 杨诺 2023 物理学报 72 034401Google Scholar
Zong Z C, Pan D K, Deng S C, Wan X, Yang L N, Ma D K, Yang N 2023 Acta Phys. Sin. 72 034401Google Scholar
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[22] Hochbaum A I, Chen R, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A, Yang P 2008 Nature 451 163Google Scholar
[23] Chen I J, Burke A, Svilans A, Linke H, Thelander C 2018 Phys. Rev. Lett. 120 177703Google Scholar
[24] Ohnishi M, Shiga T, and Shiomi J 2017 Phys. Rev. B 95 155405Google Scholar
[25] Zhou G, Li L, Li G H 2010 Appl. Phys. Lett. 97 023112Google Scholar
[26] Dash A, Scheunemann D, Kemerink M 2022 Phys. Rev. Appl. 18 064022Google Scholar
[27] Huang N T, Nugraha A R T, Saito R 2019 Energies 12 4561Google Scholar
[28] Yang N X, Yan Q, Sun Q F 2020 Phys. Rev. B 102 245412Google Scholar
[29] Tang H, Wang X, Xiong Y, Zhao Y, Zhang Y, Zhang Y, Yang J, Xu D 2015 Nanoscale 7 6683Google Scholar
[30] Fan D D, Liu H J, Cheng L, Jiang P H, Shi J, Tang X F 2014 Appl. Phys. Lett. 105 133113Google Scholar
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[33] Tang J, Chen Y, McCuskey S R, Chen L, Bazan G C, Liang Z 2019 Adv. Electron. Mater. 5 1800943Google Scholar
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[36] Liang L, Cruz-Silva E, Girão E C, Meunier V 2012 Phys. Rev. B 86 115438Google Scholar
[37] Liang L, Meunier V 2013 Appl. Phys. Lett. 102 143101Google Scholar
[38] Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401Google Scholar
[39] Mazzamuto F, Nguyen V H, Apertet Y, Caër C, Chassat C, Martin J S, Dollfus P 2011 Phys. Rev. B 83 235426Google Scholar
[40] Karamitaheri H, Neophytou N, Pourfath M, Faez R, Kosina H 2012 J. Appl. Phys. 111 054501Google Scholar
[41] Anno Y, Imakita Y, Takei K, Akita S, Arie T 2017 2D Materials 4 025019Google Scholar
[42] Xiao H, Cao W, Ouyang T, Xu X, Ding Y C, Zhong J X 2018 Appl. Phys. Lett. 112 233107Google Scholar
[43] Dollfus P, Nguyen V H, Saint-Martin J 2015 J. Phys. Condens. Matter 27 133204Google Scholar
[44] Xu Y, Li Z, Duan W 2014 Small 10 2182Google Scholar
[45] Li D, Gong Y, Chen Y, Lin J, Khan Q, Zhang Y, Li Y, Zhang H, Xie H 2020 Nano-Micro Lett. 12 36Google Scholar
[46] Hippalgaonkar K, Wang Y, Ye Y, Qiu D Y, Zhu H, Wang Y, Moore J, Louie S G, Zhang X 2017 Phys. Rev. B 95 115407Google Scholar
[47] Zhu X L, Hou C H, Zhang P, Liu P F, Xie G F, Wang B T 2020 J. Phys. Chem. C 124 1812Google Scholar
[48] Zhang G, Zhang Y W 2017 J. Mater. Chem. C 5 7684Google Scholar
[49] Zhang G, Zhang Y W 2015 Mech. Mater. 91 382Google Scholar
[50] Zeng Y J, Wu D, Cao X H, Zhou W X, Tang L M, Chen K Q 2020 Adv. Funct. Mater. 30 1903873Google Scholar
[51] Zhou D, Zhang H, Zheng H, Xu Z, Xu H, Guo H, Li P, Tong Y, Hu B, Chen L 2022 Small 18 2200679Google Scholar
[52] Hurtado-Gallego J, Sangtarash S, Davidson R, et al. 2022 Nano Lett. 22 948Google Scholar
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[55] Famili M, Grace I M, Al-Galiby Q, Sadeghi H, Lambert C J 2017 Adv. Funct. Mater. 28 1703135Google Scholar
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[57] Wu D, Cao X H, Chen S Z, Tang L M, Feng Y X, Chen K Q, Zhou W X 2019 J. Mater. Chem. A 7 19037Google Scholar
[58] Finch C, Garcia-Suarez V, Lambert C 2009 Phys. Rev. B 79 033405Google Scholar
[59] Klöckner J C, Cuevas J C, Pauly F 2017 Phys. Rev. B 96 24519Google Scholar
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[61] Hong G, Wu Q H, Ren J, Wang C, Zhang W, Lee S T 2013 Nano Today 8 388Google Scholar
[62] Zu F X, Gao G Y, Fu H H 2015 Appl. Phys. Lett. 107 252403Google Scholar
[63] Ni Y, Yao K L, Tang C Q, Gao G Y, Fu H H, Zhu S C 2014 RSC Adv. 4 18522Google Scholar
[64] Cao X H, Zhou W X, Chen C Y, Tang L M, Long M Q, Chen K Q 2017 Sci. Rep. 7 10842Google Scholar
[65] Wu D, Cao X H, Jia P Z, et al. 2020 Science. China-Phys. Mech. Astron. 63 276811Google Scholar
[66] Wang D, Tang L, Long M, Shuai Z 2011 J. Phys. Chem. C 115 5940Google Scholar
[67] Lederer J, Kaiser W, Mattoni A, Gagliardi A 2018 Adv. Theory Simul. 2 1800136Google Scholar
[68] Harada K, Sumino M, Adachi C, Tanaka S, Miyazaki K 2010 Appl. Phys. Lett. 96 253304Google Scholar
[69] Zhao W, Dai X, Liu L, Meng Q, Zou Y, Di C A, Zhu D 2021 Appl. Phys. Lett. 118 253302Google Scholar
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[71] Chen X K, Hu X Y, Jia P, Xie Z X, Liu J 2021 Int. J. Mech. Sci. 206 106576Google Scholar
[72] Ying P, Liang T, Du Y, Zhang J, Zeng X, Zhong Z 2022 Int. J. Heat Mass Transfer 183 122060Google Scholar
[73] Xie Z X, Chen X K, Yu X, Deng Y X, Zhang Y, Zhou W X, Jia P Z 2023 Comput. Mater. Sci. 220 112041Google Scholar
[74] Wang J S, Wang J, Lü J T 2008 Eur. Phys. J. B 62 381Google Scholar
[75] Watanabe S, Ohno M, Yamashita Y, Terashige T, Okamoto H, Takeya J 2019 Phys. Rev. B 100 241201(RGoogle Scholar
[76] Zhou J, Yang R 2011 Appl. Phys. Lett. 98 173107Google Scholar
[77] Cui L, Hur S, Akbar Z A, Klöckner J C, Jeong W, Pauly F, Jang S Y, Reddy P, Meyhofer E 2019 Nature 572 628Google Scholar
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图 1 并苯连接石墨烯纳米带形成分子结的几何结构示意图. 并苯分子与石墨烯纳米带电极间的接触位置用整数1, 2, 3表示. 为了方便描述, 统一用AN(mn)来表示几何结构, 其中, “N”代表并苯分子长度(也就是苯环的数目), “m, n”分别表示左电极、右电极与中间并苯分子的接触位置. 例如: 本图可以用A5(22)表示
Figure 1. Schematic geometric structure of the molecule junction formed by the acene linked with graphene nanoribbons. The contact positions between the acene molecule and graphene nanoribbon electrodes are denoted by the integers 1, 2, and 3. For the sake of description, we uniformly apply “AN(mn)” to represent the geometric structures, where “N” denotes the length of the acene molecule (namely the number of benzene rings), “m, n” denote the contact position between the left, right electrodes and the acene molecule, respectively. For example, this geometric structure is denoted by A5(22).
图 2 声子热导
$ {\sigma }_{{\rm{p}}} $ 与温度T的关系. 右下角的插图呈现了低温时声子热导$ {\sigma }_{{\rm{p}}} $ 与温度T关系的细节行为Figure 2. Phononic thermal conductance
$ {\sigma }_{{\rm{p}}} $ versus the temperature T. The bottom-right inset shows the detailed behavior of the phononic thermal conductance$ {\sigma }_{{\rm{p}}} $ versus the temperature T at low temperatures.图 4 A3(31), A3(22), A3(21)和A3(11)的(a)电导、(b) Seebeck系数、(c)热导和(d)ZT. 实线、划线、双点划线和点划线分别对应着A3(31), A3(22), A3(21)和A3(11). 图(c)中, 四条平整的曲线对应着声子热导
Figure 4. (a) Electrical conductance, (b) Seebeck coefficient, (c) thermal conductance, and (d) ZT of A3(31), A3(22), A3(21)和A3(11). The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to A3(31), A3(22), A3(21), and A3(11), respectively. In panel (c), four flat curves correspond to the phononic thermal conductance.
图 5 电子输运系数和对应的投影局域态密度. (a1)和(a2), (b1)和(b2), (c1)和(c2), (d1)和(d2)分别对应着A3(31), A3(22), A3(21), A3(11)
Figure 5. Electronic transmission coefficient and projected local density of states. (a1) and (a2), (b1) and (b2), (c1) and (c2), (d1) and (d2) correspond to A3(31), A3(22), A3(21), A3(11), respectively.
图 7 (a) 电导
$ G $ 和(b) 电子热导$ {\sigma }_{{\rm{e}}} $ 与化学势$ \mu $ 的关系. 实线、划线、双点划线、点划线分别对应着并三苯(N = 3)、并五苯(N = 5)、并七苯(N = 7)、并九苯(N = 9). 图(b)中插图表示的是温度为300 K时的声子热导Figure 7. (a) Electrical conductance and (b) electronic thermal conductance versus the versus the chemical potential
$ \mu $ . The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to anthracene (N = 3), pentacene (N = 5), heptacene (N = 7), and nonacene (N = 9). The inset in (b) denotes the phononic thermal conductance at T = 300 K.图 8 (a) Seebeck系数和(b) 热电优值ZT与化学势
$ \mu $ 的关系. 实线、划线、双点划线、点划线分别对应着并三苯(N = 3)、并五苯(N = 5)、并七苯(N = 7)、并九苯(N = 9)Figure 8. (a) Seebeck coefficient and (b)
$ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $ versus the versus the chemical potential$ \mu $ . The solid, dashed, double-dot-dashed, and dot-dashed curves correspond to anthracene (N = 3), pentacene (N = 5), heptacene (N = 7), and nonacene (N = 9), respectively.表 1 最大热电优值ZT(
$ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $ )对应的热电参数Table 1. Thermoelectric parameters corresponding to the maximum of the thermoelectric figure of merit (ZTmax).
N 接触位置 $ {ZT}_{{\rm{m}}{\rm{a}}{\rm{x}}} $ G/mS S/(mV·K–1) σp/(nW·K–1) σe/(nW·K–1) σp+σe/(nW·K–1) N = 3 (31) 0.34 0.012 –0.194 0.342 0.044 0.385 (22) 0.09 0.037 0.065 0.264 0.246 0.510 (21) 0.51 0.032 0.150 0.242 0.184 0.425 (11) 0.16 0.046 0.085 0.336 0.293 0.630 N = 5 (31) 0.28 0.015 –0.155 0.314 0.076 0.390 (22) 0.10 0.030 0.071 0.232 0.217 0.449 (21) 0.32 0.010 0.174 0.231 0.052 0.283 (11) 0.14 0.027 –0.092 0.311 0.171 0.483 N = 7 (31) 0.42 0.017 –0.178 0.305 0.080 0.385 (22) 0.23 0.025 0.103 0.210 0.144 0.350 (21) 0.44 0.012 0.183 0.221 0.053 0.274 (11) 0.40 0.017 0.176 0.304 0.086 0.390 N = 9 (31) 0.41 0.023 0.149 0.301 0.069 0.370 (22) 0.35 0.017 –0.141 0.205 0.086 0.291 (21) 0.44 0.018 –0.155 0.217 0.076 0.293 (11) 0.36 0.016 0.163 0.298 0.055 0.353 -
[1] Wu C W, Ren X, Xie G, Zhou W X, Zhang G, Chen K Q 2022 Phys. Rev. Appl. 18 014053Google Scholar
[2] Jia P Z, Xie J P, Chen X K, Zhang Y, Yu X, Zeng Y J, Xie Z X, Deng Y X, Zhou W X 2023 J. Phys. Condens. Matter 35 073001Google Scholar
[3] Li N, Ren J, Wang L, Zhang G, Hanggi P, Li B 2012 Rev. Mod. Phys. 84 1045Google Scholar
[4] Su L, Wang D, Wang S, Qin B, Wang Y, Qin Y, Jin Y, Chang C, Zhao L D 2022 Science 375 1385Google Scholar
[5] 陈晓彬, 段文晖 2015 物理学报 64 186302Google Scholar
Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302Google Scholar
[6] Jia P Z, Xie Z X, Deng Y X, Zhang Y, Tang L M, Zhou W X, Chen K Q 2022 Appl. Phys. Lett. 121 043901Google Scholar
[7] 余泽浩, 张力发, 吴靖, 赵云山 2023 物理学报 72 057301Google Scholar
Yu Z H, Zhang L F, Wu J, Zhao Y S 2023 Acta Phys. Sin. 72 057301Google Scholar
[8] Shi X L, Zou J, Chen Z G 2020 Chem. Rev. 120 7399Google Scholar
[9] Wang T, Zhang C, Snoussi H, Zhang G 2020 Adv. Funct. Mater. 30 1906041Google Scholar
[10] Xie Q Y, Ma J J, Liu Q Y, Liu P F, Zhang P, Zhang K W, Wang B T 2022 Phys. Chem. Chem. Phys. 24 7303Google Scholar
[11] Zhou Z Z, Liu H J, Fan D D, Cao G H, Sheng C Y 2019 Phys. Rev. B 99 085410Google Scholar
[12] Deng L, Chen G M 2021 Nano Energy 80 105448Google Scholar
[13] Xie Z X, Tang L M, Pan C N, Li K M, Chen K Q, Duan W 2012 Appl. Phys. Lett. 100 073105Google Scholar
[14] Ouyang Y, Guo J 2009 Appl. Phys. Lett. 94 263107Google Scholar
[15] 王艳, 陈南迪, 杨陈, 曾召益, 胡翠娥, 陈向荣 2021 物理学报 70 116301Google Scholar
Wang Y, Chen N D, Chen Y, Zeng Z Y, Hu C E, Chen X R 2021 Acta Phys. Sin. 70 116301Google Scholar
[16] Jiang J W, Wang J S, Li B 2011 J. Appl. Phys. 109 014326Google Scholar
[17] Pan H, Tang L M, Chen K Q 2022 Phys. Rev. B 105 064401Google Scholar
[18] Pan H, Ding Z K, Zeng B W, Luo N N, Zeng J, Tang L M, Chen K Q 2023 Phys. Rev. B 107 104303Google Scholar
[19] Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727Google Scholar
[20] 宗志成, 潘东楷, 邓世琛, 万骁, 杨哩娜, 马登科, 杨诺 2023 物理学报 72 034401Google Scholar
Zong Z C, Pan D K, Deng S C, Wan X, Yang L N, Ma D K, Yang N 2023 Acta Phys. Sin. 72 034401Google Scholar
[21] Markussen T, Jauho A P, Brandbyge M 2009 Phys. Rev. Lett. 103 055502Google Scholar
[22] Hochbaum A I, Chen R, Delgado R D, Liang W, Garnett E C, Najarian M, Majumdar A, Yang P 2008 Nature 451 163Google Scholar
[23] Chen I J, Burke A, Svilans A, Linke H, Thelander C 2018 Phys. Rev. Lett. 120 177703Google Scholar
[24] Ohnishi M, Shiga T, and Shiomi J 2017 Phys. Rev. B 95 155405Google Scholar
[25] Zhou G, Li L, Li G H 2010 Appl. Phys. Lett. 97 023112Google Scholar
[26] Dash A, Scheunemann D, Kemerink M 2022 Phys. Rev. Appl. 18 064022Google Scholar
[27] Huang N T, Nugraha A R T, Saito R 2019 Energies 12 4561Google Scholar
[28] Yang N X, Yan Q, Sun Q F 2020 Phys. Rev. B 102 245412Google Scholar
[29] Tang H, Wang X, Xiong Y, Zhao Y, Zhang Y, Zhang Y, Yang J, Xu D 2015 Nanoscale 7 6683Google Scholar
[30] Fan D D, Liu H J, Cheng L, Jiang P H, Shi J, Tang X F 2014 Appl. Phys. Lett. 105 133113Google Scholar
[31] Zberecki K, Wierzbicki M, Barnaś J, Swirkowicz R 2013 Phys. Rev. B 88 115404Google Scholar
[32] Liu W, Yan X, Chen G, Ren Z 2012 Nano Energy 1 42Google Scholar
[33] Tang J, Chen Y, McCuskey S R, Chen L, Bazan G C, Liang Z 2019 Adv. Electron. Mater. 5 1800943Google Scholar
[34] Foster S, Thesberg M, Neophytou N 2017 Phys. Rev. B 96 195425Google Scholar
[35] Huang W, Wang J S, Liang G 2011 Phys. Rev. B 84 045410Google Scholar
[36] Liang L, Cruz-Silva E, Girão E C, Meunier V 2012 Phys. Rev. B 86 115438Google Scholar
[37] Liang L, Meunier V 2013 Appl. Phys. Lett. 102 143101Google Scholar
[38] Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401Google Scholar
[39] Mazzamuto F, Nguyen V H, Apertet Y, Caër C, Chassat C, Martin J S, Dollfus P 2011 Phys. Rev. B 83 235426Google Scholar
[40] Karamitaheri H, Neophytou N, Pourfath M, Faez R, Kosina H 2012 J. Appl. Phys. 111 054501Google Scholar
[41] Anno Y, Imakita Y, Takei K, Akita S, Arie T 2017 2D Materials 4 025019Google Scholar
[42] Xiao H, Cao W, Ouyang T, Xu X, Ding Y C, Zhong J X 2018 Appl. Phys. Lett. 112 233107Google Scholar
[43] Dollfus P, Nguyen V H, Saint-Martin J 2015 J. Phys. Condens. Matter 27 133204Google Scholar
[44] Xu Y, Li Z, Duan W 2014 Small 10 2182Google Scholar
[45] Li D, Gong Y, Chen Y, Lin J, Khan Q, Zhang Y, Li Y, Zhang H, Xie H 2020 Nano-Micro Lett. 12 36Google Scholar
[46] Hippalgaonkar K, Wang Y, Ye Y, Qiu D Y, Zhu H, Wang Y, Moore J, Louie S G, Zhang X 2017 Phys. Rev. B 95 115407Google Scholar
[47] Zhu X L, Hou C H, Zhang P, Liu P F, Xie G F, Wang B T 2020 J. Phys. Chem. C 124 1812Google Scholar
[48] Zhang G, Zhang Y W 2017 J. Mater. Chem. C 5 7684Google Scholar
[49] Zhang G, Zhang Y W 2015 Mech. Mater. 91 382Google Scholar
[50] Zeng Y J, Wu D, Cao X H, Zhou W X, Tang L M, Chen K Q 2020 Adv. Funct. Mater. 30 1903873Google Scholar
[51] Zhou D, Zhang H, Zheng H, Xu Z, Xu H, Guo H, Li P, Tong Y, Hu B, Chen L 2022 Small 18 2200679Google Scholar
[52] Hurtado-Gallego J, Sangtarash S, Davidson R, et al. 2022 Nano Lett. 22 948Google Scholar
[53] Reddy P, Jang S Y, Segalman R A, Majumdar A 2007 Science 315 1568Google Scholar
[54] Miao R, Xu H, Skripnik M, Cui L, et al. 2018 Nano Lett. 18 5666Google Scholar
[55] Famili M, Grace I M, Al-Galiby Q, Sadeghi H, Lambert C J 2017 Adv. Funct. Mater. 28 1703135Google Scholar
[56] Bürkle M, Hellmuth T J, Pauly F, Asai Y 2015 Phys. Rev. B 91 165419Google Scholar
[57] Wu D, Cao X H, Chen S Z, Tang L M, Feng Y X, Chen K Q, Zhou W X 2019 J. Mater. Chem. A 7 19037Google Scholar
[58] Finch C, Garcia-Suarez V, Lambert C 2009 Phys. Rev. B 79 033405Google Scholar
[59] Klöckner J C, Cuevas J C, Pauly F 2017 Phys. Rev. B 96 24519Google Scholar
[60] Ratner M 2013 Nat. Nanotechnol. 8 378Google Scholar
[61] Hong G, Wu Q H, Ren J, Wang C, Zhang W, Lee S T 2013 Nano Today 8 388Google Scholar
[62] Zu F X, Gao G Y, Fu H H 2015 Appl. Phys. Lett. 107 252403Google Scholar
[63] Ni Y, Yao K L, Tang C Q, Gao G Y, Fu H H, Zhu S C 2014 RSC Adv. 4 18522Google Scholar
[64] Cao X H, Zhou W X, Chen C Y, Tang L M, Long M Q, Chen K Q 2017 Sci. Rep. 7 10842Google Scholar
[65] Wu D, Cao X H, Jia P Z, et al. 2020 Science. China-Phys. Mech. Astron. 63 276811Google Scholar
[66] Wang D, Tang L, Long M, Shuai Z 2011 J. Phys. Chem. C 115 5940Google Scholar
[67] Lederer J, Kaiser W, Mattoni A, Gagliardi A 2018 Adv. Theory Simul. 2 1800136Google Scholar
[68] Harada K, Sumino M, Adachi C, Tanaka S, Miyazaki K 2010 Appl. Phys. Lett. 96 253304Google Scholar
[69] Zhao W, Dai X, Liu L, Meng Q, Zou Y, Di C A, Zhu D 2021 Appl. Phys. Lett. 118 253302Google Scholar
[70] Krüger J, García F, Eisenhut F, et al. 2017 Angew. Chem. Int. Ed. 56 11945Google Scholar
[71] Chen X K, Hu X Y, Jia P, Xie Z X, Liu J 2021 Int. J. Mech. Sci. 206 106576Google Scholar
[72] Ying P, Liang T, Du Y, Zhang J, Zeng X, Zhong Z 2022 Int. J. Heat Mass Transfer 183 122060Google Scholar
[73] Xie Z X, Chen X K, Yu X, Deng Y X, Zhang Y, Zhou W X, Jia P Z 2023 Comput. Mater. Sci. 220 112041Google Scholar
[74] Wang J S, Wang J, Lü J T 2008 Eur. Phys. J. B 62 381Google Scholar
[75] Watanabe S, Ohno M, Yamashita Y, Terashige T, Okamoto H, Takeya J 2019 Phys. Rev. B 100 241201(RGoogle Scholar
[76] Zhou J, Yang R 2011 Appl. Phys. Lett. 98 173107Google Scholar
[77] Cui L, Hur S, Akbar Z A, Klöckner J C, Jeong W, Pauly F, Jang S Y, Reddy P, Meyhofer E 2019 Nature 572 628Google Scholar
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