搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

陈晓彬 段文晖

引用本文:
Citation:

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

陈晓彬, 段文晖

Quantum thermal transport and spin thermoelectrics in low-dimensional nano systems: application of nonequilibrium Green's function method

Chen Xiao-Bin, Duan Wen-Hui
PDF
导出引用
  • 低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.
    Emerging novel properties of nanomaterials have been attracting attention. Besides quantum electronic transport properties, the breakdown of classical Fourier’s law and other significant quantum thermal behaviors such as quantized thermal conductance, phonon subbands, size effects, the bottleneck effect, and even interaction between heat and spin degrees of freedom have also been revealed over the past two decades. These phenomena can be well captured by the nonequilibrium Green’s function (NEGF) method, which is pretty simple under ballistic or quasi-ballistic regimes. In this review, we mainly focus on two aspects: quantum phonon transport and thermal-spin transport in low-dimensional nanostructures. First, we present a brief history of researches on thermal transport in nanostructures, summarize basic characteristics of quantum thermal transport, and then describe the basic algorithm and framework of the phonon NEGF method. Compared with other methods, the NEGF method facilitates numerical calculations and can systematically incorporate quantum many-body effects. We further demonstrate the power of phonon NEGF method by recent research progress: from the phonon NEGF method, distinct behaviors of phonon transport compared with those of electrons, intrinsic anisotropy of phonon transport, radial strain within elastic regime as quantum perturbation, two kinds of interfacial transport behaviors, defect-induced localization of local phonon density of states, unobservable phonon localization, etc, have been discovered in some particular low-dimensional nanomaterials or nanostructures. Second, the new concept of “spin caloritronics”, which is devoted to the study of thermally induced spin-related transport in magnetic systems and offers a brand-new way to realize thermal-spin or thermoelectric energy conversion, is also introduced. After concisely discussing the spin Seebeck effect, spin-dependent Seebeck effect, and magneto-Seebeck effect, we present the linear response theory with spin degree of freedom and show that by combining with linear response theory, NEGF method is also applicable for studying spin caloritronics, especially spin thermoelectrics. Finally, recent research on quantum dot models or numerical calculation of real materials give hints to the searching for high-ZT materials. With the ever-increasing demand for energy and increasing power density in highly integrated circuits, quantum thermal transport properties are not only of fundamental interest, but also crucial for future developing electronic devices. Relevant researches also pave the way to spin thermoelectrics, which has vast potential in thermoelectric spintronic devices and energy harvesting.
      通信作者: 段文晖, dwh@phys.tsinghua.edu.cn
    • 基金项目: 国家重点基础研究发展计划(批准号: 2011CB921901, 2011CB606405)和国家自然科学基金(批准号:11334006)资助的课题.
      Corresponding author: Duan Wen-Hui, dwh@phys.tsinghua.edu.cn
    • Funds: Project supported by the National Basic Research Program of China (Grant Nos. 2011CB921901, 2011CB606405), the National Natural Science Foundation of China (Grant No. 11334006).
    [1]

    Pop E, Sinha S, Goodson K 2006 Proc. IEEE 94 1587

    [2]
    [3]

    Hu M, Keblinski P, Wang J S, Raravikar N 2008 J. Appl. Phys. 104 083503

    [4]

    Chu S, Majumdar A 2012 Nature 488 294

    [5]

    Hochbaum A, Chen R, Delgado R, Liang W, Garnett E, Najarian M, Majumdar A, Yang P 2008 Nature 451 163

    [6]

    Dresselhaus M S, Chen G, Tang M Y, Yang R G, Lee H, Wang D Z, Ren Z F, Fleurial J P, Gogna P 2007 Adv. Mater. 19 1043

    [7]

    Schwab K, Henriksen E, Worlock J, Roukes M 2000 Nature 404 974

    [8]

    Hone J, Batlogg B, Benes Z, Johnson A, Fischer J 2000 Science 289 1730

    [9]

    Pendry J 1983 J. Phys. A: Math. Gen. 16 2161

    [10]

    Angelescu D, Cross M, Roukes M 1998 Superlattice. Microstruct. 23 673

    [11]

    Blencowe M 1999 Phys. Rev. B 59 4992

    [12]

    Maynard R, Akkermans E 1985 Phys. Rev. B 32 5440

    [13]

    Rego L G C, Kirczenow G 1998 Phys. Rev. Lett. 81 232

    [14]

    Yamamoto T, Watanabe S, Watanabe K 2004 Phys. Rev. Lett. 92 075502

    [15]

    Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727

    [16]

    Siemens M E, Li Q, Yang R, Nelson K A, Anderson E H, Murnane M M, Kapteyn H C 2010 Nat. Mater. 9 26

    [17]

    Xu Y 2010 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [徐勇 2010 博士学位论文 (北京: 清华大学)]

    [18]

    Liu S, Xu X, Xie R, Zhang G, Li B 2012 Eur. Phys. J. B 85 1

    [19]

    Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896

    [20]

    Garrido P L, Hurtado P I, Nadrowski B 2001 Phys. Rev. Lett. 86 5486

    [21]

    Li B, Wang L, Hu B 2002 Phys. Rev. Lett. 88 223901

    [22]

    Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601

    [23]

    Livi R, Lepri S 2003 Nature 421 327

    [24]

    Saito K 2003 Europhys. Lett. 61 34

    [25]

    Michel M, Mahler G, Gemmer J 2005 Phys. Rev. Lett. 95 180602

    [26]

    Zhao H 2006 Phys. Rev. Lett. 96 140602

    [27]

    Bricmont J, Kupiainen A 2007 Phys. Rev. Lett. 98 214301

    [28]

    Dhar A, Lebowitz J L 2008 Phys. Rev. Lett. 100 134301

    [29]

    Chang C, Okawa D, Garcia H, Majumdar A, Zettl A 2008 Phys. Rev. Lett. 101 75903

    [30]

    Yang N, Zhang G, Li B 2010 Nano Today 5 85

    [31]

    Guo Z, Zhang D, Gong X G 2009 Appl. Phys. Lett. 95 163103

    [32]

    Xu X, Pereira L F C, Wang Y, Wu J, Zhang K, Zhao X, Bae S, Tinh Bui C, Xie R, Thong J T L, Hong B H, Loh K P, Donadio D, Li B, Özyilmaz B 2014 Nat. Commun. 5 3689

    [33]

    Volz S G, Chen G 1999 Appl. Phys. Lett. 75 2056

    [34]

    Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A 2003 Appl. Phys. Lett. 83 2934

    [35]

    Chen S, Moore A L, Cai W, Suk J W, An J, Mishra C, Amos C, Magnuson C W, Kang J, Shi L, Ruoff R S 2011 ACS Nano 5 321

    [36]

    Balandin A A 2011 Nat. Mater. 10 569

    [37]

    Chen S, Wu Q, Mishra C, Kang J, Zhang H, Cho K, Cai W, Balandin A A, Ruoff R S 2012 Nat. Mater. 11 203

    [38]

    Pop E, Varshney V, Roy A K 2012 Mrs. Bull. 37 1273

    [39]

    Hone J, Whitney M, Piskoti C, Zettl A 1999 Phys. Rev. B 59 2514

    [40]

    Kim P, Shi L, Majumdar A, McEuen P L 2001 Phys. Rev. Lett. 87 215502

    [41]

    Yu C, Shi L, Yao Z, Li D, Majumdar A 2005 Nano Lett. 5 1842

    [42]

    Fujii M, Zhang X, Xie H, Ago H, Takahashi K, Ikuta T, Abe H, Shimizu T 2005 Phys. Rev. Lett. 95 065502

    [43]

    Li Q, Liu C, Wang X, Fan S 2009 Nanotechnology 20 145702

    [44]

    Pop E, Mann D, Wang Q, Goodson K, Dai H 2006 Nano Lett. 6 96

    [45]

    Saito R, Dresselhaus G, Dresselhaus M 1998 Physical Properties of Carbon Nanotubes (London: Imperial College)

    [46]

    Munõz E, Lu J, Yakobson B 2010 Nano Lett. 10 1652

    [47]

    Chen K Q, Duan W, Gu B L, Gu B Y 2002 Phys. Lett. A 299 634

    [48]

    Peng X F, Wang X J, Gong Z Q, Chen K Q 2011 Appl. Phys. Lett. 99 233105

    [49]

    Li W X, Chen K Q, Duan W, Wu J, Gu B L 2003 Phys. Lett. A 308 285

    [50]

    Mahan G D 1987 Phys. Rep. 145 251

    [51]

    Donadio D, Galli G 2007 Phys. Rev. Lett. 99 255502

    [52]

    Broido D A, Malorny M, Birner G, Mingo N, Stewart D A 2007 Appl. Phys. Lett. 91 231922

    [53]

    Lindsay L, Broido D A, Mingo N 2009 Phys. Rev. B 80 125407

    [54]

    Lindsay L, Broido D A, Mingo N 2010 Phys. Rev. B 82 161402

    [55]

    Lindsay L, Broido D, Mingo N 2010 Phys. Rev. B 82 115427

    [56]

    Li N, Ren J, Wang L, Zhang G, Hänggi P, Li B 2012 Rev. Mod. Phys. 84 1045

    [57]

    Zhang G 2013 Nanoscale Energy Transport and Harvesting: A Computational Study (Singapore: Pan Stanford Publishing)

    [58]

    Cao B Y, Li Y W 2010 J. Chem. Phys. 133 024106

    [59]

    Wei N, Xu L, Wang H Q, Zheng J C 2011 Nanotechnology 22 105705

    [60]

    Cao H Y, Guo Z X, Xiang H, Gong X G 2012 Phys. Lett. A 376 525

    [61]

    Yao W J, Cao B Y, Yun H M, Chen B M 2014 Nanoscale Res. Lett. 9 408

    [62]

    Xu Y, Li Z, Duan W 2014 Small 10 2182

    [63]

    Ozpineci A, Ciraci S 2001 Phys. Rev. B 63 125415

    [64]

    Mingo N, Yang L 2003 Phys. Rev. B 68 245406

    [65]

    Yamamoto T, Watanabe K 2006 Phys. Rev. Lett. 96 255503

    [66]

    Wang J S, Wang J, Zeng N 2006 Phys. Rev. B 74 033408

    [67]

    Cahill D G, Ford W K, Goodson K E, Mahan G D, Majumdar A, Maris H J, Merlin R, Phillpot S R 2003 J. Appl. Phys. 93 793

    [68]

    Dubi Y, Di Ventra M 2009 Phys. Rev. E 79 042101

    [69]

    Hopkins P E, Norris P M, Tsegaye M S, Ghosh A W 2009 J. Appl. Phys. 106 063503

    [70]

    Xu Y, Wang J S, Duan W, Gu B L, Li B 2008 Phys. Rev. B 78 224303

    [71]

    Wang J S, Wang J, L J 2008 Eur. Phys. J. B 62 381

    [72]

    Dubi Y, Di Ventra M 2011 Rev. Mod. Phys. 83 131

    [73]

    Chen X, Liu D, Duan W, Guo H 2013 Phys. Rev. B 87 085427

    [74]

    Hu J, Ruan X, Chen Y 2009 Nano Lett. 9 2730

    [75]

    Brenner D, Shenderova O, Harrison J, Stuart S, Ni B, Sinnott S 2002 J. Phys.: Condens. Matter 14 783

    [76]

    Jishi R A, Venkataraman L, Dresselhaus M S, Dresselhaus G 1993 Chem. Phys. Lett. 209 77

    [77]

    Mingo N, Stewart D A, Broido D A, Srivastava D 2008 Phys. Rev. B 77 033418

    [78]

    Ren J, Hänggi P, Li B, Chiatti O, Nicholls J T, Proskuryakov Y Y, Lumpkin N, Farrer I, Ritchie D A 2006 Phys. Rev. Lett. 97 056601

    [79]

    Meschke M, Guichard W, Pekola J P 2006 Nature 444 187

    [80]

    Xu Y, Chen X, Wang J S, Gu B L, Duan W 2010 Phys. Rev. B 81 195425

    [81]

    Zhang D, Liu L, Bao Z, Xiao H, Zhang Y 2013 Physica E 53 110

    [82]

    Mingo N, Broido D A 2005 Phys. Rev. Lett. 95 096105

    [83]

    Xu Y, Chen X, Gu B L, Duan W 2009 Appl. Phys. Lett. 95 233116

    [84]

    Tan Z, Wang J, Gan C 2011 Nano Lett. 11 214

    [85]

    Li D, Xu Y, Chen X, Li B, Duan W 2014 Appl. Phys. Lett. 104 143108

    [86]

    Ouyang T, Chen Y, Liu L M, Xie Y, Wei X, Zhong J 2012 Phys. Rev. B 85 235436

    [87]

    Zhou G, Duan W, Gu B 2001 Chem. Phys. Lett. 333 344

    [88]

    Zhou G, Duan W, Gu B 2001 Phys. Rev. Lett. 87 095504

    [89]

    Falvo M R, Clary G J, Taylor R M, Chi V, Brooks F P, Washburn S, Superfine R 1997 Nature 389 582

    [90]

    Zhu H, Xu Y, Gu B L, Duan W 2012 New J. Phys. 14 013053

    [91]

    Chang C W, Okawa D, Garcia H, Majumdar A, Zettl A 2007 Phys. Rev. Lett. 99 045901

    [92]

    Ouyang T, Chen Y, Xie Y, Stocks G M, Zhong J 2011 Appl. Phys. Lett. 99 233101

    [93]

    Li D, Li B, Luo M, Feng C, Ouyang T, Gao F 2013 Appl. Phys. Lett. 103 071908

    [94]

    Yang N, Ni X, Jiang J W, Li B 2012 Appl. Phys. Lett. 100 093107

    [95]

    Chen X, Xu Y, Zou X, Gu B L, Duan W 2013 Phys. Rev. B 87 155438

    [96]

    Huang Z, Fisher T S, Murthy J Y 2010 J. Appl. Phys. 108 114310

    [97]

    Xu Y, Chen X, Wang J S, Gu B L, Duan W 2010 Phys. Rev. B 81 195425

    [98]

    Huang H, Xu Y, Zou X, Wu J, Duan W 2013 Phys. Rev. B 87 205415

    [99]

    Tan S H, Tang L M, Xie Z X, Pan C N, Chen K Q 2013 Carbon 65 181

    [100]

    Lu Y, Guo J 2012 Appl. Phys. Lett. 101 043112

    [101]

    Zhang G, Li B 2010 Nanoscale 2 1058

    [102]

    Morooka M, Yamamoto T, Watanabe K 2008 Phys. Rev. B 77 033412

    [103]

    Wang J, Wang J S 2009 J. Appl. Phys. 105 063509

    [104]

    Xie Z X, Tang L M, Pan C N, Li K M, Chen K Q, Duan W 2012 Appl. Phys. Lett. 100 073105

    [105]

    Jiang J W, Wang B S, Wang J S 2011 Appl. Phys. Lett. 98 113114

    [106]

    Peng X F, Chen K Q 2014 Carbon 77 360

    [107]

    Wang J, Li L, Wang J S 2011 Appl. Phys. Lett. 99 091905

    [108]

    Scuracchio P, Costamagna S, Peeters F M, Dobry A 2014 Phys. Rev. B 90 035429

    [109]

    Cheng Y Q, Zhou S Y, Zhu B F 2005 Phys. Rev. B 72 035410

    [110]

    Zhang G, Li B 2005 J. Chem. Phys. 123 114714

    [111]

    Yang N, Zhang G, Li B 2008 Nano Lett. 8 276

    [112]

    Ni X, Leek M L, Wang J S, Feng Y P, Li B W 2011 Phys. Rev. B 83 045408

    [113]

    Savic I, Mingo N, Stewart D A 2008 Phys. Rev. Lett. 101 165502

    [114]

    Li W X, Chen K Q, Duan W, Wu J, Gu B L 2004 Appl. Phys. Lett. 85 822

    [115]

    Zhang D, Bao Z, Su J, Tang C, Zang C, Zhang Y 2012 Physica B 407 4333

    [116]

    Peng X F, Xiong C, Wang X J, Chen L Q, Luo Y F, Li J B 2013 Comp. Mater. Sci. 77 440

    [117]

    Chang C, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121

    [118]

    Yang N, Zhang G, Li B 2009 Appl. Phys. Lett. 95 033107

    [119]

    Xie Z X, Li K M, Tang L M, Pan C N, Chen K Q 2012 Appl. Phys. Lett. 100 183110

    [120]

    Zhang J Z, Zhu B F 2006 J. Appl. Phys. 100 013707

    [121]

    Chen Y, Regnault N, Ferreira R, Zhu B F, Bastard G 2009 Phys. Rev. B 79 235314

    [122]

    Padgett C W, Brenner D W 2004 Nano Lett. 4 1051

    [123]

    Seol J, Jo I, Moore A, Lindsay L, Aitken Z, Pettes M, Li X, Yao Z, Huang R, Broido D 2010 Science 328 213

    [124]

    Guo Z X, Zhang D, Gong X G 2011 Phys. Rev. B 84 075470

    [125]

    Ong Z Y, Pop E 2011 Phys. Rev. B 84 075471

    [126]

    Ioffe A 1957 Semiconductor Thermoelements, and Thermoelectric Cooling (London: Infosearch ltd.)

    [127]

    Murphy P, Mukerjee S, Moore J 2008 Phys. Rev. B 78 161406

    [128]

    Snyder G J, Toberer E S 2008 Nat. Mater. 7 105

    [129]

    Cutler M, Mott N F 1969 Phys. Rev. 181 1336

    [130]

    Paulsson M, Datta S 2003 Phys. Rev. B 67 241403

    [131]

    Reddy P, Jang S Y, Segalman R A, Majumdar A 2007 Science 315 1568

    [132]

    Mazzamuto F, Hung Nguyen V, Apertet Y, Caër C, Chassat C, Saint-Martin J, Dollfus P 2011 Phys. Rev. B 83 235426

    [133]

    Saha K K, Markussen T, Thygesen K S, Nikolić B K 2011 Phys. Rev. B 84 041412

    [134]

    Majumdar A 2004 Science 303 777

    [135]

    Hicks L D, Harman T C, Sun X, Dresselhaus M S 1996 Phys. Rev. B 53 R10493

    [136]

    Harman T, Taylor P, Walsh M, LaForge B 2002 Science 297 2229

    [137]

    Heremans J P, Jovovic V, Toberer E S, Saramat A, Kurosaki K, Charoenphakdee A, Yamanaka S, Snyder G J 2008 Science 321 554

    [138]

    Lin Y M, Dresselhaus M 2003 Phys. Rev. B 68 075304

    [139]

    Liu J, Sun Q F, Xie X 2010 Phys. Rev. B 81 245323

    [140]

    Zhou J, Yang R, Chen G, Dresselhaus M S 2011 Phys. Rev. Lett. 107 226601

    [141]

    L\""u H Y, Lu W J, Shao D F, Sun Y P 2014 Phys. Rev. B 90 085433

    [142]

    Boukai A, Bunimovich Y, Tahir-Kheli J, Yu J, Goddard Iii W, Heath J 2008 Nature 451 168

    [143]

    Poudel B, Hao Q, Ma Y, Lan Y, Minnich A, Yu B, Yan X, Wang D, Muto A, Vashaee D, Chen X, Liu J, Dresselhaus M S, Chen G, Ren Z 2008 Science 320 634

    [144]

    Mingo N 2004 Appl. Phys. Lett. 84 2652

    [145]

    Markussen T, Jauho A P, Brandbyge M 2009 Phys. Rev. Lett. 103 055502

    [146]

    Ni X, Liang G, Wang J S, Li B 2009 Appl. Phys. Lett. 95 192114

    [147]

    Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401

    [148]

    Gunst T, Markussen T, Jauho A P, Brandbyge M 2011 Phys. Rev. B 84 155449

    [149]

    Huang W, Wang J S, Liang G 2011 Phys. Rev. B 84 045410

    [150]

    Zou X, Chen X, Huang H, Xu Y, Duan W 2015 Nanoscale 7 8776

    [151]

    Bhat R R, Nastos F, Najmaie A, Sipe J 2005 Phys. Rev. Lett. 94 096603

    [152]

    Chen J, Hu Y, Guo H, Chen X 2014 J. Phys.: Condens. Matter 26 016003

    [153]

    Wang B, Wang J, Guo H 2003 Phys. Rev. B 67 092408

    [154]

    Brataas A, Tserkovnyak Y, Bauer G E W, Halperin B I 2002 Phys. Rev. B 66 060404

    [155]

    Uchida K, Takahashi S, Harii K, Ieda J, Koshibae W, Ando K, Maekawa S, Saitoh E 2008 Nature 455 778

    [156]

    Bauer G E W, Saitoh E, Wees B J 2012 Nat. Mater. 11 391

    [157]

    Boona S R, Myers R C, Heremans J P 2014 Energy Environ. Sci. 7 885

    [158]

    Johnson M 2010 Solid State Commun. 150 543

    [159]

    Zheng J S, Zheng J C 2014 Mater. Sci. 4 175(in Chinese) [郑建森, 郑金成 2014 材料科学 4 175]

    [160]

    Rowe D M

    [161]

    Goyal V, Teweldebrhan D, Balandin A A 2010 Appl. Phys. Lett. 97 133117

    [162]

    Hiroto A, Ken-ichi U, Eiji S, Sadamichi M 2013 Rep. Prog. Phys. 76 036501

    [163]

    Xiao J, Bauer G, Uchida K, Saitoh E, Maekawa S 2010 Phys. Rev. B 81 214418

    [164]

    Uchida K, Xiao J, Adachi H, Ohe J, Takahashi S, Ieda J, Ota T, Kajiwara Y, Umezawa H, Kawai H, Bauer G E W, Maekawa S, Saitoh E 2010 Nat. Mater. 9 894

    [165]

    Bosu S, Sakuraba Y, Uchida K, Saito K, Ota T, Saitoh E, Takanashi K 2011 Phys. Rev. B 83 224401

    [166]

    Jaworski C M, Yang J, Mack S, Awschalom D D, Heremans J P, Myers R C 2010 Nat. Mater. 9 898

    [167]

    Uchida K, Adachi H, An T, Ota T, Toda M, Hillebrands B, Maekawa S, Saitoh E 2011 Nat. Mater. 10 737

    [168]

    Uchida K, Adachi H, Ota T, Nakayama H, Maekawa S, Saitoh E 2010 Appl. Phys. Lett. 97 172505

    [169]

    Weiler M, Althammer M, Czeschka F D, Huebl H, Wagner M S, Opel M, Imort I M, Reiss G, Thomas A, Gross R, Goennenwein S T B 2012 Phys. Rev. Lett. 108 106602

    [170]

    Niizeki T, Kikkawa T, Uchida K I, Oka M, Suzuki K Z, Yanagihara H, Kita E, Saitoh E 2015 AIP Adv. 5 053603

    [171]

    Dejene F K, Flipse J, Bauer G E W, Wees B J 2013 Nat. Phys. 9 636

    [172]

    Gravier L, Serrano-Guisan S, Reuse F, Ansermet J P 2006 Phys. Rev. B 73 052410

    [173]

    Slachter A, Bakker F, Adam J, van Wees B 2010 Nat. Phys. 6 879

    [174]

    Flipse J, Bakker F L, Slachter A, Dejene F K, Wees B J 2012 Nat. Nano 7 166

    [175]

    Dejene F, Flipse J, van Wees B 2012 Phys. Rev. B 86 024436

    [176]

    Le Breton J, Sharma S, Saito H, Yuasa S, Jansen R 2011 Nature 475 82

    [177]

    Waldron D, Timoshevskii V, Hu Y, Xia K, Guo H 2006 Phys. Rev. Lett. 97 226802

    [178]

    Walter M, Walowski J, Zbarsky V, Mnzenberg M, Schäfers M, Ebke D, Reiss G, Thomas A, Peretzki P, Seibt M, Moodera J S, Czerner M, Bachmann M, Heiliger C 2011 Nat. Mater. 10 742

    [179]

    Teixeira J M, Costa J D, Ventura J, Fernandez-Garcia M P, Azevedo J, Araujo J P, Sousa J B, Wisniowski P, Cardoso S, Freitas P P 2013 Appl. Phys. Lett. 102 212413

    [180]

    Liebing N, Serrano-Guisan S, Rott K, Reiss G, Langer J, Ocker B, Schumacher H W 2011 Phys. Rev. Lett. 107 177201

    [181]

    Swirkowicz R, Wierzbicki M, Barnas J 2009 Phys. Rev. B 80 195409

    [182]

    Czerner M, Bachmann M, Heiliger C 2011 Phys. Rev. B 83 132405

    [183]

    Lin W, Hehn M, Chaput L, Negulescu B, Andrieu S, Montaigne F, Mangin S 2012 Nat. Commun. 3 744

    [184]

    Jain S, Lam D D, Bose A, Sharma H, Palkar V R, Tomy C V, Suzuki Y, Tulapurkar A A 2014 AIP Adv. 4 127145

    [185]

    Wang Z 2007 Thermal Dynamics·Statistical Physics (3rd Ed.) (Beijing: Higher Education Press) (in Chinese) [汪志诚 2007 热力学·统计物理学(第三版)(北京:高等教育出版社)]

    [186]

    Johnson M, Silsbee R H 1987 Phys. Rev. B 35 4959

    [187]

    Takezoe Y, Hosono K, Takeuchi A, Tatara G 2010 Phys. Rev. B 82 094451

    [188]

    Uchida K, Takahashi S, Harii K, Ieda J, Koshibae W, Ando K, Maekawa S, Saitoh E 2008 Nature 455 778

    [189]

    Dubi Y, Di Ventra M 2009 Phys. Rev. B 79 081302

    [190]

    Slachter A, Bakker F, Adam J, van Wees B 2010 Nat. Phys. 6 879

    [191]

    Rejec T, Žitko R, Mravlje J, Ramšak A 2012 Phys. Rev. B 85 085117

    [192]

    Cahaya A B, Tretiakov O A, Bauer G 2015 arXiv preprint arXiv:1504.02002

    [193]

    Liao T, Lin J, Su G, Lin B, Chen J 2015 Nanoscale DOI: 10.1039/c5nr01738f

    [194]

    Wierzbicki M, Świrkowicz R 2010 Phys. Rev. B 82 165334

    [195]

    Zheng J, Chi F, Guo Y 2012 J. Phys.: Condens. Matter 24 265301

    [196]

    Jiang F, Xie H, Yan Y 2014 Phys. Lett. A 378 1854

    [197]

    Ghosh A, Frota H 2014 Eur. Phys. J. B 87 1

    [198]

    Liu J, Cheng J, Wang S 2014 Phys. Scripta 89 085701

    [199]

    Dong S, Niu Z P 2015 Phys. Lett. A 379 443

    [200]

    Hwang S Y, López R, Lee M, Sánchez D 2014 Phys. Rev. B 90 115301

    [201]

    Chen S G 2012 J. Phys.: Condens. Matter 24 385302

    [202]

    Wierzbicki M, Swirkowicz R, Barnaś J 2013 Phys. Rev. B 88 235434

    [203]

    Zberecki K, Swirkowicz R, J B 2014 Phys. Rev. B 89 165419

    [204]

    Liu Y S, Zhou W Q, Feng J F, Wang X F 2015 Chem. Phys. Lett. 625 14

    [205]

    Zhai M X, Wang X F, Vasilopoulos P, Liu Y S, Dong Y J, Zhou L, Jiang Y J, You W L 2014 Nanoscale 6 11121

    [206]

    Yang X, Liu Y, Zhang X, Zhou L, Wang X, Chi F, Feng J 2014 Phys. Chem. Chem. Phys. 16 11349

    [207]

    Liu Y, Zhang X, Yang X, Hong X, Feng J, Si M, Wang X 2015 Phys. Chem. Chem. Phys. 17 10462

    [208]

    Wu Q, Zhao P, Su Y, Liu D, Chen G 2015 RSC Adv. 5 20699

    [209]

    Zhou B, Zhou B, Zeng Y, Zhou G, Ouyang T 2015 J. Appl. Phys. 117 104305

    [210]

    Chen X, Liu Y, Gu B L, Duan W, Liu F 2014 Phys. Rev. B 90 121403

    [211]

    Geim A K, Grigorieva I V 2013 Nature 499 419

    [212]

    Chen X, Tian F, Persson C, Duan W, Chen N X 2013 Sci. Rep. 3 3046

    [213]

    Lui C H, Ye Z, Ji C, Chiu K C, Chou C T, Andersen T I, Means-Shively C, Anderson H, Wu J M, Kidd T, Lee Y H, He R 2015 Phys. Rev. B 91 165403

    [214]

    Ren J, Hänggi P, Li B 2010 Phys. Rev. Lett. 104 170601

    [215]

    Xiao M, Ma G, Yang Z, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240

    [216]

    Wang J, Deng S, Liu Z, Liu Z 2015 Natl. Sci. Rev. 2 22

    [217]

    Li Y, Chen X 2015 2D Mater. 1 031002

  • [1]

    Pop E, Sinha S, Goodson K 2006 Proc. IEEE 94 1587

    [2]
    [3]

    Hu M, Keblinski P, Wang J S, Raravikar N 2008 J. Appl. Phys. 104 083503

    [4]

    Chu S, Majumdar A 2012 Nature 488 294

    [5]

    Hochbaum A, Chen R, Delgado R, Liang W, Garnett E, Najarian M, Majumdar A, Yang P 2008 Nature 451 163

    [6]

    Dresselhaus M S, Chen G, Tang M Y, Yang R G, Lee H, Wang D Z, Ren Z F, Fleurial J P, Gogna P 2007 Adv. Mater. 19 1043

    [7]

    Schwab K, Henriksen E, Worlock J, Roukes M 2000 Nature 404 974

    [8]

    Hone J, Batlogg B, Benes Z, Johnson A, Fischer J 2000 Science 289 1730

    [9]

    Pendry J 1983 J. Phys. A: Math. Gen. 16 2161

    [10]

    Angelescu D, Cross M, Roukes M 1998 Superlattice. Microstruct. 23 673

    [11]

    Blencowe M 1999 Phys. Rev. B 59 4992

    [12]

    Maynard R, Akkermans E 1985 Phys. Rev. B 32 5440

    [13]

    Rego L G C, Kirczenow G 1998 Phys. Rev. Lett. 81 232

    [14]

    Yamamoto T, Watanabe S, Watanabe K 2004 Phys. Rev. Lett. 92 075502

    [15]

    Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727

    [16]

    Siemens M E, Li Q, Yang R, Nelson K A, Anderson E H, Murnane M M, Kapteyn H C 2010 Nat. Mater. 9 26

    [17]

    Xu Y 2010 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese) [徐勇 2010 博士学位论文 (北京: 清华大学)]

    [18]

    Liu S, Xu X, Xie R, Zhang G, Li B 2012 Eur. Phys. J. B 85 1

    [19]

    Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896

    [20]

    Garrido P L, Hurtado P I, Nadrowski B 2001 Phys. Rev. Lett. 86 5486

    [21]

    Li B, Wang L, Hu B 2002 Phys. Rev. Lett. 88 223901

    [22]

    Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601

    [23]

    Livi R, Lepri S 2003 Nature 421 327

    [24]

    Saito K 2003 Europhys. Lett. 61 34

    [25]

    Michel M, Mahler G, Gemmer J 2005 Phys. Rev. Lett. 95 180602

    [26]

    Zhao H 2006 Phys. Rev. Lett. 96 140602

    [27]

    Bricmont J, Kupiainen A 2007 Phys. Rev. Lett. 98 214301

    [28]

    Dhar A, Lebowitz J L 2008 Phys. Rev. Lett. 100 134301

    [29]

    Chang C, Okawa D, Garcia H, Majumdar A, Zettl A 2008 Phys. Rev. Lett. 101 75903

    [30]

    Yang N, Zhang G, Li B 2010 Nano Today 5 85

    [31]

    Guo Z, Zhang D, Gong X G 2009 Appl. Phys. Lett. 95 163103

    [32]

    Xu X, Pereira L F C, Wang Y, Wu J, Zhang K, Zhao X, Bae S, Tinh Bui C, Xie R, Thong J T L, Hong B H, Loh K P, Donadio D, Li B, Özyilmaz B 2014 Nat. Commun. 5 3689

    [33]

    Volz S G, Chen G 1999 Appl. Phys. Lett. 75 2056

    [34]

    Li D, Wu Y, Kim P, Shi L, Yang P, Majumdar A 2003 Appl. Phys. Lett. 83 2934

    [35]

    Chen S, Moore A L, Cai W, Suk J W, An J, Mishra C, Amos C, Magnuson C W, Kang J, Shi L, Ruoff R S 2011 ACS Nano 5 321

    [36]

    Balandin A A 2011 Nat. Mater. 10 569

    [37]

    Chen S, Wu Q, Mishra C, Kang J, Zhang H, Cho K, Cai W, Balandin A A, Ruoff R S 2012 Nat. Mater. 11 203

    [38]

    Pop E, Varshney V, Roy A K 2012 Mrs. Bull. 37 1273

    [39]

    Hone J, Whitney M, Piskoti C, Zettl A 1999 Phys. Rev. B 59 2514

    [40]

    Kim P, Shi L, Majumdar A, McEuen P L 2001 Phys. Rev. Lett. 87 215502

    [41]

    Yu C, Shi L, Yao Z, Li D, Majumdar A 2005 Nano Lett. 5 1842

    [42]

    Fujii M, Zhang X, Xie H, Ago H, Takahashi K, Ikuta T, Abe H, Shimizu T 2005 Phys. Rev. Lett. 95 065502

    [43]

    Li Q, Liu C, Wang X, Fan S 2009 Nanotechnology 20 145702

    [44]

    Pop E, Mann D, Wang Q, Goodson K, Dai H 2006 Nano Lett. 6 96

    [45]

    Saito R, Dresselhaus G, Dresselhaus M 1998 Physical Properties of Carbon Nanotubes (London: Imperial College)

    [46]

    Munõz E, Lu J, Yakobson B 2010 Nano Lett. 10 1652

    [47]

    Chen K Q, Duan W, Gu B L, Gu B Y 2002 Phys. Lett. A 299 634

    [48]

    Peng X F, Wang X J, Gong Z Q, Chen K Q 2011 Appl. Phys. Lett. 99 233105

    [49]

    Li W X, Chen K Q, Duan W, Wu J, Gu B L 2003 Phys. Lett. A 308 285

    [50]

    Mahan G D 1987 Phys. Rep. 145 251

    [51]

    Donadio D, Galli G 2007 Phys. Rev. Lett. 99 255502

    [52]

    Broido D A, Malorny M, Birner G, Mingo N, Stewart D A 2007 Appl. Phys. Lett. 91 231922

    [53]

    Lindsay L, Broido D A, Mingo N 2009 Phys. Rev. B 80 125407

    [54]

    Lindsay L, Broido D A, Mingo N 2010 Phys. Rev. B 82 161402

    [55]

    Lindsay L, Broido D, Mingo N 2010 Phys. Rev. B 82 115427

    [56]

    Li N, Ren J, Wang L, Zhang G, Hänggi P, Li B 2012 Rev. Mod. Phys. 84 1045

    [57]

    Zhang G 2013 Nanoscale Energy Transport and Harvesting: A Computational Study (Singapore: Pan Stanford Publishing)

    [58]

    Cao B Y, Li Y W 2010 J. Chem. Phys. 133 024106

    [59]

    Wei N, Xu L, Wang H Q, Zheng J C 2011 Nanotechnology 22 105705

    [60]

    Cao H Y, Guo Z X, Xiang H, Gong X G 2012 Phys. Lett. A 376 525

    [61]

    Yao W J, Cao B Y, Yun H M, Chen B M 2014 Nanoscale Res. Lett. 9 408

    [62]

    Xu Y, Li Z, Duan W 2014 Small 10 2182

    [63]

    Ozpineci A, Ciraci S 2001 Phys. Rev. B 63 125415

    [64]

    Mingo N, Yang L 2003 Phys. Rev. B 68 245406

    [65]

    Yamamoto T, Watanabe K 2006 Phys. Rev. Lett. 96 255503

    [66]

    Wang J S, Wang J, Zeng N 2006 Phys. Rev. B 74 033408

    [67]

    Cahill D G, Ford W K, Goodson K E, Mahan G D, Majumdar A, Maris H J, Merlin R, Phillpot S R 2003 J. Appl. Phys. 93 793

    [68]

    Dubi Y, Di Ventra M 2009 Phys. Rev. E 79 042101

    [69]

    Hopkins P E, Norris P M, Tsegaye M S, Ghosh A W 2009 J. Appl. Phys. 106 063503

    [70]

    Xu Y, Wang J S, Duan W, Gu B L, Li B 2008 Phys. Rev. B 78 224303

    [71]

    Wang J S, Wang J, L J 2008 Eur. Phys. J. B 62 381

    [72]

    Dubi Y, Di Ventra M 2011 Rev. Mod. Phys. 83 131

    [73]

    Chen X, Liu D, Duan W, Guo H 2013 Phys. Rev. B 87 085427

    [74]

    Hu J, Ruan X, Chen Y 2009 Nano Lett. 9 2730

    [75]

    Brenner D, Shenderova O, Harrison J, Stuart S, Ni B, Sinnott S 2002 J. Phys.: Condens. Matter 14 783

    [76]

    Jishi R A, Venkataraman L, Dresselhaus M S, Dresselhaus G 1993 Chem. Phys. Lett. 209 77

    [77]

    Mingo N, Stewart D A, Broido D A, Srivastava D 2008 Phys. Rev. B 77 033418

    [78]

    Ren J, Hänggi P, Li B, Chiatti O, Nicholls J T, Proskuryakov Y Y, Lumpkin N, Farrer I, Ritchie D A 2006 Phys. Rev. Lett. 97 056601

    [79]

    Meschke M, Guichard W, Pekola J P 2006 Nature 444 187

    [80]

    Xu Y, Chen X, Wang J S, Gu B L, Duan W 2010 Phys. Rev. B 81 195425

    [81]

    Zhang D, Liu L, Bao Z, Xiao H, Zhang Y 2013 Physica E 53 110

    [82]

    Mingo N, Broido D A 2005 Phys. Rev. Lett. 95 096105

    [83]

    Xu Y, Chen X, Gu B L, Duan W 2009 Appl. Phys. Lett. 95 233116

    [84]

    Tan Z, Wang J, Gan C 2011 Nano Lett. 11 214

    [85]

    Li D, Xu Y, Chen X, Li B, Duan W 2014 Appl. Phys. Lett. 104 143108

    [86]

    Ouyang T, Chen Y, Liu L M, Xie Y, Wei X, Zhong J 2012 Phys. Rev. B 85 235436

    [87]

    Zhou G, Duan W, Gu B 2001 Chem. Phys. Lett. 333 344

    [88]

    Zhou G, Duan W, Gu B 2001 Phys. Rev. Lett. 87 095504

    [89]

    Falvo M R, Clary G J, Taylor R M, Chi V, Brooks F P, Washburn S, Superfine R 1997 Nature 389 582

    [90]

    Zhu H, Xu Y, Gu B L, Duan W 2012 New J. Phys. 14 013053

    [91]

    Chang C W, Okawa D, Garcia H, Majumdar A, Zettl A 2007 Phys. Rev. Lett. 99 045901

    [92]

    Ouyang T, Chen Y, Xie Y, Stocks G M, Zhong J 2011 Appl. Phys. Lett. 99 233101

    [93]

    Li D, Li B, Luo M, Feng C, Ouyang T, Gao F 2013 Appl. Phys. Lett. 103 071908

    [94]

    Yang N, Ni X, Jiang J W, Li B 2012 Appl. Phys. Lett. 100 093107

    [95]

    Chen X, Xu Y, Zou X, Gu B L, Duan W 2013 Phys. Rev. B 87 155438

    [96]

    Huang Z, Fisher T S, Murthy J Y 2010 J. Appl. Phys. 108 114310

    [97]

    Xu Y, Chen X, Wang J S, Gu B L, Duan W 2010 Phys. Rev. B 81 195425

    [98]

    Huang H, Xu Y, Zou X, Wu J, Duan W 2013 Phys. Rev. B 87 205415

    [99]

    Tan S H, Tang L M, Xie Z X, Pan C N, Chen K Q 2013 Carbon 65 181

    [100]

    Lu Y, Guo J 2012 Appl. Phys. Lett. 101 043112

    [101]

    Zhang G, Li B 2010 Nanoscale 2 1058

    [102]

    Morooka M, Yamamoto T, Watanabe K 2008 Phys. Rev. B 77 033412

    [103]

    Wang J, Wang J S 2009 J. Appl. Phys. 105 063509

    [104]

    Xie Z X, Tang L M, Pan C N, Li K M, Chen K Q, Duan W 2012 Appl. Phys. Lett. 100 073105

    [105]

    Jiang J W, Wang B S, Wang J S 2011 Appl. Phys. Lett. 98 113114

    [106]

    Peng X F, Chen K Q 2014 Carbon 77 360

    [107]

    Wang J, Li L, Wang J S 2011 Appl. Phys. Lett. 99 091905

    [108]

    Scuracchio P, Costamagna S, Peeters F M, Dobry A 2014 Phys. Rev. B 90 035429

    [109]

    Cheng Y Q, Zhou S Y, Zhu B F 2005 Phys. Rev. B 72 035410

    [110]

    Zhang G, Li B 2005 J. Chem. Phys. 123 114714

    [111]

    Yang N, Zhang G, Li B 2008 Nano Lett. 8 276

    [112]

    Ni X, Leek M L, Wang J S, Feng Y P, Li B W 2011 Phys. Rev. B 83 045408

    [113]

    Savic I, Mingo N, Stewart D A 2008 Phys. Rev. Lett. 101 165502

    [114]

    Li W X, Chen K Q, Duan W, Wu J, Gu B L 2004 Appl. Phys. Lett. 85 822

    [115]

    Zhang D, Bao Z, Su J, Tang C, Zang C, Zhang Y 2012 Physica B 407 4333

    [116]

    Peng X F, Xiong C, Wang X J, Chen L Q, Luo Y F, Li J B 2013 Comp. Mater. Sci. 77 440

    [117]

    Chang C, Okawa D, Majumdar A, Zettl A 2006 Science 314 1121

    [118]

    Yang N, Zhang G, Li B 2009 Appl. Phys. Lett. 95 033107

    [119]

    Xie Z X, Li K M, Tang L M, Pan C N, Chen K Q 2012 Appl. Phys. Lett. 100 183110

    [120]

    Zhang J Z, Zhu B F 2006 J. Appl. Phys. 100 013707

    [121]

    Chen Y, Regnault N, Ferreira R, Zhu B F, Bastard G 2009 Phys. Rev. B 79 235314

    [122]

    Padgett C W, Brenner D W 2004 Nano Lett. 4 1051

    [123]

    Seol J, Jo I, Moore A, Lindsay L, Aitken Z, Pettes M, Li X, Yao Z, Huang R, Broido D 2010 Science 328 213

    [124]

    Guo Z X, Zhang D, Gong X G 2011 Phys. Rev. B 84 075470

    [125]

    Ong Z Y, Pop E 2011 Phys. Rev. B 84 075471

    [126]

    Ioffe A 1957 Semiconductor Thermoelements, and Thermoelectric Cooling (London: Infosearch ltd.)

    [127]

    Murphy P, Mukerjee S, Moore J 2008 Phys. Rev. B 78 161406

    [128]

    Snyder G J, Toberer E S 2008 Nat. Mater. 7 105

    [129]

    Cutler M, Mott N F 1969 Phys. Rev. 181 1336

    [130]

    Paulsson M, Datta S 2003 Phys. Rev. B 67 241403

    [131]

    Reddy P, Jang S Y, Segalman R A, Majumdar A 2007 Science 315 1568

    [132]

    Mazzamuto F, Hung Nguyen V, Apertet Y, Caër C, Chassat C, Saint-Martin J, Dollfus P 2011 Phys. Rev. B 83 235426

    [133]

    Saha K K, Markussen T, Thygesen K S, Nikolić B K 2011 Phys. Rev. B 84 041412

    [134]

    Majumdar A 2004 Science 303 777

    [135]

    Hicks L D, Harman T C, Sun X, Dresselhaus M S 1996 Phys. Rev. B 53 R10493

    [136]

    Harman T, Taylor P, Walsh M, LaForge B 2002 Science 297 2229

    [137]

    Heremans J P, Jovovic V, Toberer E S, Saramat A, Kurosaki K, Charoenphakdee A, Yamanaka S, Snyder G J 2008 Science 321 554

    [138]

    Lin Y M, Dresselhaus M 2003 Phys. Rev. B 68 075304

    [139]

    Liu J, Sun Q F, Xie X 2010 Phys. Rev. B 81 245323

    [140]

    Zhou J, Yang R, Chen G, Dresselhaus M S 2011 Phys. Rev. Lett. 107 226601

    [141]

    L\""u H Y, Lu W J, Shao D F, Sun Y P 2014 Phys. Rev. B 90 085433

    [142]

    Boukai A, Bunimovich Y, Tahir-Kheli J, Yu J, Goddard Iii W, Heath J 2008 Nature 451 168

    [143]

    Poudel B, Hao Q, Ma Y, Lan Y, Minnich A, Yu B, Yan X, Wang D, Muto A, Vashaee D, Chen X, Liu J, Dresselhaus M S, Chen G, Ren Z 2008 Science 320 634

    [144]

    Mingo N 2004 Appl. Phys. Lett. 84 2652

    [145]

    Markussen T, Jauho A P, Brandbyge M 2009 Phys. Rev. Lett. 103 055502

    [146]

    Ni X, Liang G, Wang J S, Li B 2009 Appl. Phys. Lett. 95 192114

    [147]

    Sevinçli H, Cuniberti G 2010 Phys. Rev. B 81 113401

    [148]

    Gunst T, Markussen T, Jauho A P, Brandbyge M 2011 Phys. Rev. B 84 155449

    [149]

    Huang W, Wang J S, Liang G 2011 Phys. Rev. B 84 045410

    [150]

    Zou X, Chen X, Huang H, Xu Y, Duan W 2015 Nanoscale 7 8776

    [151]

    Bhat R R, Nastos F, Najmaie A, Sipe J 2005 Phys. Rev. Lett. 94 096603

    [152]

    Chen J, Hu Y, Guo H, Chen X 2014 J. Phys.: Condens. Matter 26 016003

    [153]

    Wang B, Wang J, Guo H 2003 Phys. Rev. B 67 092408

    [154]

    Brataas A, Tserkovnyak Y, Bauer G E W, Halperin B I 2002 Phys. Rev. B 66 060404

    [155]

    Uchida K, Takahashi S, Harii K, Ieda J, Koshibae W, Ando K, Maekawa S, Saitoh E 2008 Nature 455 778

    [156]

    Bauer G E W, Saitoh E, Wees B J 2012 Nat. Mater. 11 391

    [157]

    Boona S R, Myers R C, Heremans J P 2014 Energy Environ. Sci. 7 885

    [158]

    Johnson M 2010 Solid State Commun. 150 543

    [159]

    Zheng J S, Zheng J C 2014 Mater. Sci. 4 175(in Chinese) [郑建森, 郑金成 2014 材料科学 4 175]

    [160]

    Rowe D M

    [161]

    Goyal V, Teweldebrhan D, Balandin A A 2010 Appl. Phys. Lett. 97 133117

    [162]

    Hiroto A, Ken-ichi U, Eiji S, Sadamichi M 2013 Rep. Prog. Phys. 76 036501

    [163]

    Xiao J, Bauer G, Uchida K, Saitoh E, Maekawa S 2010 Phys. Rev. B 81 214418

    [164]

    Uchida K, Xiao J, Adachi H, Ohe J, Takahashi S, Ieda J, Ota T, Kajiwara Y, Umezawa H, Kawai H, Bauer G E W, Maekawa S, Saitoh E 2010 Nat. Mater. 9 894

    [165]

    Bosu S, Sakuraba Y, Uchida K, Saito K, Ota T, Saitoh E, Takanashi K 2011 Phys. Rev. B 83 224401

    [166]

    Jaworski C M, Yang J, Mack S, Awschalom D D, Heremans J P, Myers R C 2010 Nat. Mater. 9 898

    [167]

    Uchida K, Adachi H, An T, Ota T, Toda M, Hillebrands B, Maekawa S, Saitoh E 2011 Nat. Mater. 10 737

    [168]

    Uchida K, Adachi H, Ota T, Nakayama H, Maekawa S, Saitoh E 2010 Appl. Phys. Lett. 97 172505

    [169]

    Weiler M, Althammer M, Czeschka F D, Huebl H, Wagner M S, Opel M, Imort I M, Reiss G, Thomas A, Gross R, Goennenwein S T B 2012 Phys. Rev. Lett. 108 106602

    [170]

    Niizeki T, Kikkawa T, Uchida K I, Oka M, Suzuki K Z, Yanagihara H, Kita E, Saitoh E 2015 AIP Adv. 5 053603

    [171]

    Dejene F K, Flipse J, Bauer G E W, Wees B J 2013 Nat. Phys. 9 636

    [172]

    Gravier L, Serrano-Guisan S, Reuse F, Ansermet J P 2006 Phys. Rev. B 73 052410

    [173]

    Slachter A, Bakker F, Adam J, van Wees B 2010 Nat. Phys. 6 879

    [174]

    Flipse J, Bakker F L, Slachter A, Dejene F K, Wees B J 2012 Nat. Nano 7 166

    [175]

    Dejene F, Flipse J, van Wees B 2012 Phys. Rev. B 86 024436

    [176]

    Le Breton J, Sharma S, Saito H, Yuasa S, Jansen R 2011 Nature 475 82

    [177]

    Waldron D, Timoshevskii V, Hu Y, Xia K, Guo H 2006 Phys. Rev. Lett. 97 226802

    [178]

    Walter M, Walowski J, Zbarsky V, Mnzenberg M, Schäfers M, Ebke D, Reiss G, Thomas A, Peretzki P, Seibt M, Moodera J S, Czerner M, Bachmann M, Heiliger C 2011 Nat. Mater. 10 742

    [179]

    Teixeira J M, Costa J D, Ventura J, Fernandez-Garcia M P, Azevedo J, Araujo J P, Sousa J B, Wisniowski P, Cardoso S, Freitas P P 2013 Appl. Phys. Lett. 102 212413

    [180]

    Liebing N, Serrano-Guisan S, Rott K, Reiss G, Langer J, Ocker B, Schumacher H W 2011 Phys. Rev. Lett. 107 177201

    [181]

    Swirkowicz R, Wierzbicki M, Barnas J 2009 Phys. Rev. B 80 195409

    [182]

    Czerner M, Bachmann M, Heiliger C 2011 Phys. Rev. B 83 132405

    [183]

    Lin W, Hehn M, Chaput L, Negulescu B, Andrieu S, Montaigne F, Mangin S 2012 Nat. Commun. 3 744

    [184]

    Jain S, Lam D D, Bose A, Sharma H, Palkar V R, Tomy C V, Suzuki Y, Tulapurkar A A 2014 AIP Adv. 4 127145

    [185]

    Wang Z 2007 Thermal Dynamics·Statistical Physics (3rd Ed.) (Beijing: Higher Education Press) (in Chinese) [汪志诚 2007 热力学·统计物理学(第三版)(北京:高等教育出版社)]

    [186]

    Johnson M, Silsbee R H 1987 Phys. Rev. B 35 4959

    [187]

    Takezoe Y, Hosono K, Takeuchi A, Tatara G 2010 Phys. Rev. B 82 094451

    [188]

    Uchida K, Takahashi S, Harii K, Ieda J, Koshibae W, Ando K, Maekawa S, Saitoh E 2008 Nature 455 778

    [189]

    Dubi Y, Di Ventra M 2009 Phys. Rev. B 79 081302

    [190]

    Slachter A, Bakker F, Adam J, van Wees B 2010 Nat. Phys. 6 879

    [191]

    Rejec T, Žitko R, Mravlje J, Ramšak A 2012 Phys. Rev. B 85 085117

    [192]

    Cahaya A B, Tretiakov O A, Bauer G 2015 arXiv preprint arXiv:1504.02002

    [193]

    Liao T, Lin J, Su G, Lin B, Chen J 2015 Nanoscale DOI: 10.1039/c5nr01738f

    [194]

    Wierzbicki M, Świrkowicz R 2010 Phys. Rev. B 82 165334

    [195]

    Zheng J, Chi F, Guo Y 2012 J. Phys.: Condens. Matter 24 265301

    [196]

    Jiang F, Xie H, Yan Y 2014 Phys. Lett. A 378 1854

    [197]

    Ghosh A, Frota H 2014 Eur. Phys. J. B 87 1

    [198]

    Liu J, Cheng J, Wang S 2014 Phys. Scripta 89 085701

    [199]

    Dong S, Niu Z P 2015 Phys. Lett. A 379 443

    [200]

    Hwang S Y, López R, Lee M, Sánchez D 2014 Phys. Rev. B 90 115301

    [201]

    Chen S G 2012 J. Phys.: Condens. Matter 24 385302

    [202]

    Wierzbicki M, Swirkowicz R, Barnaś J 2013 Phys. Rev. B 88 235434

    [203]

    Zberecki K, Swirkowicz R, J B 2014 Phys. Rev. B 89 165419

    [204]

    Liu Y S, Zhou W Q, Feng J F, Wang X F 2015 Chem. Phys. Lett. 625 14

    [205]

    Zhai M X, Wang X F, Vasilopoulos P, Liu Y S, Dong Y J, Zhou L, Jiang Y J, You W L 2014 Nanoscale 6 11121

    [206]

    Yang X, Liu Y, Zhang X, Zhou L, Wang X, Chi F, Feng J 2014 Phys. Chem. Chem. Phys. 16 11349

    [207]

    Liu Y, Zhang X, Yang X, Hong X, Feng J, Si M, Wang X 2015 Phys. Chem. Chem. Phys. 17 10462

    [208]

    Wu Q, Zhao P, Su Y, Liu D, Chen G 2015 RSC Adv. 5 20699

    [209]

    Zhou B, Zhou B, Zeng Y, Zhou G, Ouyang T 2015 J. Appl. Phys. 117 104305

    [210]

    Chen X, Liu Y, Gu B L, Duan W, Liu F 2014 Phys. Rev. B 90 121403

    [211]

    Geim A K, Grigorieva I V 2013 Nature 499 419

    [212]

    Chen X, Tian F, Persson C, Duan W, Chen N X 2013 Sci. Rep. 3 3046

    [213]

    Lui C H, Ye Z, Ji C, Chiu K C, Chou C T, Andersen T I, Means-Shively C, Anderson H, Wu J M, Kidd T, Lee Y H, He R 2015 Phys. Rev. B 91 165403

    [214]

    Ren J, Hänggi P, Li B 2010 Phys. Rev. Lett. 104 170601

    [215]

    Xiao M, Ma G, Yang Z, Sheng P, Zhang Z Q, Chan C T 2015 Nat. Phys. 11 240

    [216]

    Wang J, Deng S, Liu Z, Liu Z 2015 Natl. Sci. Rev. 2 22

    [217]

    Li Y, Chen X 2015 2D Mater. 1 031002

  • [1] 贺艳斌, 白熙. 一维线性非共轭石墨烯基(CH2)n分子链的电子输运. 物理学报, 2021, 70(4): 046201. doi: 10.7498/aps.70.20200953
    [2] 梁锦涛, 颜晓红, 张影, 肖杨. 硼或氮掺杂的锯齿型石墨烯纳米带的非共线磁序与电子输运性质. 物理学报, 2019, 68(2): 027101. doi: 10.7498/aps.68.20181754
    [3] 吴宇, 蔡绍洪, 邓明森, 孙光宇, 刘文江. 聚噻吩单链量子热输运的第一性原理研究. 物理学报, 2018, 67(2): 026501. doi: 10.7498/aps.67.20171198
    [4] 俎凤霞, 张盼盼, 熊伦, 殷勇, 刘敏敏, 高国营. 以石墨烯为电极的有机噻吩分子整流器的设计及电输运特性研究. 物理学报, 2017, 66(9): 098501. doi: 10.7498/aps.66.098501
    [5] 周欣, 高仁斌, 谭仕华, 彭小芳, 蒋湘涛, 包本刚. 多空穴错位分布对石墨纳米带中热输运的影响. 物理学报, 2017, 66(12): 126302. doi: 10.7498/aps.66.126302
    [6] 吴宇, 蔡绍洪, 邓明森, 孙光宇, 刘文江, 岑超. 聚乙烯单链量子热输运的同位素效应. 物理学报, 2017, 66(11): 116501. doi: 10.7498/aps.66.116501
    [7] 柳福提, 张淑华, 程艳, 陈向荣, 程晓洪. (GaAs)n(n=1-4)原子链电子输运性质的理论计算. 物理学报, 2016, 65(10): 106201. doi: 10.7498/aps.65.106201
    [8] 卿前军, 周欣, 谢芳, 陈丽群, 王新军, 谭仕华, 彭小芳. 多通道石墨纳米带中弹性声学声子输运和热导特性. 物理学报, 2016, 65(8): 086301. doi: 10.7498/aps.65.086301
    [9] 白继元, 贺泽龙, 李立, 韩桂华, 张彬林, 姜平晖, 樊玉环. 两端线型双量子点分子Aharonov-Bohm干涉仪电输运. 物理学报, 2015, 64(20): 207304. doi: 10.7498/aps.64.207304
    [10] 柳福提, 程艳, 陈向荣, 程晓洪, 曾志强. Au-Si60-Au分子结电子输运性质的理论计算. 物理学报, 2014, 63(17): 177304. doi: 10.7498/aps.63.177304
    [11] 贺泽龙, 白继元, 李鹏, 吕天全. T型双量子点分子Aharonov-Bohm干涉仪的电输运. 物理学报, 2014, 63(22): 227304. doi: 10.7498/aps.63.227304
    [12] 白继元, 贺泽龙, 杨守斌. 平行耦合双量子点分子A-B干涉仪的电荷及其自旋输运. 物理学报, 2014, 63(1): 017303. doi: 10.7498/aps.63.017303
    [13] 柳福提, 程艳, 羊富彬, 程晓洪, 陈向荣. Si4团簇电子输运性质的第一性原理计算 . 物理学报, 2013, 62(14): 140504. doi: 10.7498/aps.62.140504
    [14] 柳福提, 程艳, 羊富彬, 程晓洪, 陈向荣. Au-Si-Au结点电子输运性质的第一性原理计算. 物理学报, 2013, 62(10): 107401. doi: 10.7498/aps.62.107401
    [15] 黄耀清, 郝成红, 郑继明, 任兆玉. 硅团簇自旋电子器件的理论研究. 物理学报, 2013, 62(8): 083601. doi: 10.7498/aps.62.083601
    [16] 安兴涛, 穆惠英, 咸立芬, 刘建军. 量子点双链中电子自旋极化输运性质. 物理学报, 2012, 61(15): 157201. doi: 10.7498/aps.61.157201
    [17] 琚鑫, 郭健宏. 点间耦合强度对三耦合量子点系统微分电导的影响. 物理学报, 2011, 60(5): 057302. doi: 10.7498/aps.60.057302
    [18] 邱明, 张振华, 邓小清. 碳链输运对基团吸附的敏感性分析. 物理学报, 2010, 59(6): 4162-4169. doi: 10.7498/aps.59.4162
    [19] 郑新亮, 郑继明, 任兆玉, 郭平, 田进寿, 白晋涛. 钽硅团簇电子输运性质的第一性原理研究. 物理学报, 2009, 58(8): 5709-5715. doi: 10.7498/aps.58.5709
    [20] 郑小宏, 戴振翔, 王贤龙, 曾雉. B与N掺杂对单层石墨纳米带自旋极化输运的影响. 物理学报, 2009, 58(13): 259-S265. doi: 10.7498/aps.58.259
计量
  • 文章访问数:  5923
  • PDF下载量:  912
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-05-18
  • 修回日期:  2015-06-20
  • 刊出日期:  2015-09-05

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

    基金项目: 国家重点基础研究发展计划(批准号: 2011CB921901, 2011CB606405)和国家自然科学基金(批准号:11334006)资助的课题.

摘要: 低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.

English Abstract

参考文献 (217)

目录

    /

    返回文章
    返回