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By using the nonequilibrium Green's function method, the ballistic thermal rectification in the three-terminal graphene nanojunction is studied. The dynamics of atoms is described by the interatomic fourth-nearest neighbor force-constant model. The nanojunction has a Y-shaped structure, created by a combination of a straight graphene nanoribbon and a leaning branch as the control terminal holding a fixed temperature. No heat flux flows through the control terminal. There exists a temperature bias between the two ends of the graphene nanoribbon serving as the left and right terminals, respectively. The primary goal of this paper is to demonstrate that the ballistic thermal rectification can be introduced by the asymmetric structure with different connection angles between terminals. The control terminal has a smaller connection angle with respect to the left terminal than to the right terminal. The forward direction is defined as being from the left terminal to the right terminal. The results demonstrate that, given the same control temperature and absolute temperature bias, the heat flux in the graphene nanoribbon tends to run preferentially along the forward direction. When the difference between the connection angles increases, the rectification ratio rises. Compared with that of the zigzag graphene nanoribbon, the rectification ratio of the armchair nanoribbon is much sensitive to the direction the control terminal. However, the greatest rectification ratio is found in the zigzag graphene nanoribbon which has a connection angle of 30 degrees with respect to the armchair branch. In addition, the direction of the control terminal can be adjusted to raise more than 50% of the rectification ratio of the graphene thermal rectifier based on the width discrepancy between the left and right terminals. The mechanism of the ballistic thermal rectification is also discussed. In the three-terminal graphene nanojunction, a smaller connection angle with respect to the control terminal leads to more phonon scatterings. The confirmation of this conclusion comes from a comparison of phonon transmission between different couples of terminals, which shows that in most of the frequency spectrum, the phonon transmission between the control terminal and the left terminal is smaller than between the control terminal and the right terminal. Given the same control terminal temperature and temperature bias, the asymmetric connection angles therefore will introduce a higher average temperature of the left and right terminals, and a larger heat flux in the forward process. Moreover, the average temperature difference between in the forward process and in the reverse process is found to be proportional to the temperature bias, and the proportionality coefficient will become bigger if the asymmetry is strengthened.
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[3] Li B W, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301
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[12] Wang Y, Chen S Y, Ruan X L 2012 Appl. Phys. Lett. 100 163101
[13] Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Carbon 100 492
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[24] Xu Y, Chen X B, Wang J S, Gu B L, Duan W H 2010 Phys. Rev. B 81 195425
[25] Bao Z G, Chen Y P, Ouyang T, Yang K K, Zhong J X 2011 Acta Phys. Sin. 60 028103 (in Chinese)[鲍志刚, 陈元平, 欧阳滔, 杨凯科, 钟建新2011 60 028103]
[26] Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302 (in Chinese)[陈晓彬, 段文晖2015 64 186302]
[27] Saito R, Dresselhaus G, Dresselhaus M S 1998 Physical Properties of Carbon Nanotubes (London:Imperial College Press) pp166-171
[28] Pourfath M 2014 Non-equilibrium Green's Function Method for Nanoscale Device Simulation (Wien:Springer-Verlag) pp221-230
[29] Scuracchio P, Dobry A, Costamagna S, Peeters F M 2015 Nanotechnology 26 305401
[30] Wang J S, Wang J, L J T 2008 Eur. Phys. J. B 62 381
[31] Roberts N A, Walker D G 2011 Int. J. Therm. Sci. 50 648
[32] Zhang G 2015 Nanoscale Energy Transport and Harvesting:A Computational Study (Boca Raton:CRC Press) pp91-141
[33] Li X, Wang X, Zhang L, Lee S, Dai H 2008 Science 319 1229
[34] Balandin A A 2011 Nat. Mater. 10 569
[35] Munoz E, Lu J, Yakobson B I 2010 Nano Lett. 10 1652
[36] Kim T Y, Park C H, Marzari N 2016 Nano Lett. 16 2439
[37] Ye E J, Sui W Q, Zhao X A 2012 Appl. Phys. Lett. 100 193303
[38] Chen Y P, Xie Y E, Yan X H 2008 J. Appl. Phys. 103 063711
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[1] Maldovan M 2013 Nature 503 209
[2] Terraneo M, Peyrard M, Casati G 2002 Phys. Rev. Lett. 88 094302
[3] Li B W, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301
[4] Chang C W, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121
[5] Scheibner R, König M, Reuter D, Wieck A D, Buhmann H, Molenkamp L W 2007 New J. Phys. 10 083016
[6] Tian H, Xie D, Yang Y, Ren T L, Zhang G, Wang Y F, Zhou C J, Peng P G, Wang L G, Liu L T 2012 Sci. Rep. 2 523
[7] Zeng N, Wang J S 2008 Phys. Rev. B 78 024305
[8] Yang N, Li N B, Wang L, Li B W 2007 Phys. Rev. B 76 020301
[9] Shah T N, Gajjar P N 2013 Eur. Phys. J. B 86 497
[10] Yang N, Zhang G, Li B W 2008 Appl. Phys. Lett. 93 243111
[11] Wang Y, Vallabhaneni A, Hu J N, Qiu B, Chen Y P, Ruan X L 2014 Nano Lett. 14 592
[12] Wang Y, Chen S Y, Ruan X L 2012 Appl. Phys. Lett. 100 163101
[13] Chen X K, Xie Z X, Zhou W X, Tang L M, Chen K Q 2016 Carbon 100 492
[14] Ding X, Ming Y 2014 Chin. Phys. Lett. 31 046601
[15] Ouyang T, Chen Y P, Xie Y E, Wei X L, Yang K K, Yang P, Zhong J X 2010 Phys. Rev. B 82 245403
[16] Liang B, Yuan Y, Cheng J C 2015 Acta Phys. Sin. 64 094305 (in Chinese)[梁彬, 袁樱, 程建春2015 64 094305]
[17] Ming Y, Wang Z X, Ding Z J, Li H M 2010 New J. Phys. 12 103041
[18] Zhang L F, Wang J S, Li B W 2010 Phys. Rev. B 81 100301
[19] Xie Z X, Li K M, Tang L M, Pan C N, Chen K Q 2012 Appl. Phys. Lett. 100 183110
[20] Gu Y F, Ni Z H, Chen M H, Bi K D, Chen Y F 2012 J. Heat Trans. 134 062401
[21] Ghosh S, Calizo I, Teweldebrhan D, Pokatilov E P, Nika D L, Balandin A A, Bao W, Miao F, Lau C N 2008 Appl. Phys. Lett. 92 151911
[22] Zhang Y, Liu L Q, Xi N, Wang Y C, Dong Z L 2012 Sci. Sin.:Phys. Mech. Astron. 42 358 (in Chinese)[张嵛, 刘连庆, 席宁, 王越超, 董再励2012中国科学:物理学力学天文学 42 358]
[23] Areshkin D A, White C T 2007 Nano Lett. 7 3253
[24] Xu Y, Chen X B, Wang J S, Gu B L, Duan W H 2010 Phys. Rev. B 81 195425
[25] Bao Z G, Chen Y P, Ouyang T, Yang K K, Zhong J X 2011 Acta Phys. Sin. 60 028103 (in Chinese)[鲍志刚, 陈元平, 欧阳滔, 杨凯科, 钟建新2011 60 028103]
[26] Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302 (in Chinese)[陈晓彬, 段文晖2015 64 186302]
[27] Saito R, Dresselhaus G, Dresselhaus M S 1998 Physical Properties of Carbon Nanotubes (London:Imperial College Press) pp166-171
[28] Pourfath M 2014 Non-equilibrium Green's Function Method for Nanoscale Device Simulation (Wien:Springer-Verlag) pp221-230
[29] Scuracchio P, Dobry A, Costamagna S, Peeters F M 2015 Nanotechnology 26 305401
[30] Wang J S, Wang J, L J T 2008 Eur. Phys. J. B 62 381
[31] Roberts N A, Walker D G 2011 Int. J. Therm. Sci. 50 648
[32] Zhang G 2015 Nanoscale Energy Transport and Harvesting:A Computational Study (Boca Raton:CRC Press) pp91-141
[33] Li X, Wang X, Zhang L, Lee S, Dai H 2008 Science 319 1229
[34] Balandin A A 2011 Nat. Mater. 10 569
[35] Munoz E, Lu J, Yakobson B I 2010 Nano Lett. 10 1652
[36] Kim T Y, Park C H, Marzari N 2016 Nano Lett. 16 2439
[37] Ye E J, Sui W Q, Zhao X A 2012 Appl. Phys. Lett. 100 193303
[38] Chen Y P, Xie Y E, Yan X H 2008 J. Appl. Phys. 103 063711
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