Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2021, Vol. 16 Issue (4): 43201   https://doi.org/10.1007/s11467-021-1051-3
  本期目录
A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach
Zhi-Zhou Yu, Guo-Huan Xiong, Li-Fa Zhang()
NNU-SULI Thermal Energy Research Center (NSTER) & Center for Quantum Transport and Thermal Energy Science (CQTES), School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
 全文: PDF(3290 KB)  
Abstract

With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green’s function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects. For the aspect of phonon transport, the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains, multi-terminal systems, and transient phonon transport are discussed. For the aspect of thermoelectric transport, the caloritronic effects in which the charge, spin, and valley degrees of freedom are manipulated by the temperature gradient are discussed. The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.

Key wordsthermal transport    nonequilibrium Green’s function
收稿日期: 2020-12-29      出版日期: 2021-04-12
Corresponding Author(s): Li-Fa Zhang   
 引用本文:   
. [J]. Frontiers of Physics, 2021, 16(4): 43201.
Zhi-Zhou Yu, Guo-Huan Xiong, Li-Fa Zhang. A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach. Front. Phys. , 2021, 16(4): 43201.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-021-1051-3
https://academic.hep.com.cn/fop/CN/Y2021/V16/I4/43201
1 E. Pop, S. Sinha, and K. E. Goodson, Heat generation and transport in nanometer-scale transistors, Proc. IEEE 94(8), 1587 (2006)
https://doi.org/10.1109/JPROC.2006.879794
2 N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, and B. Li, Phononics: Manipulating heat flow with electronic analogs and beyond, Rev. Mod. Phys. 84(3), 1045 (2012)
https://doi.org/10.1103/RevModPhys.84.1045
3 G. Zhang and Y. W. Zhang, Thermal properties of two-dimensional materials, Chin. Phys. B 26(3), 034401 (2017)
https://doi.org/10.1088/1674-1056/26/3/034401
4 X. Chen, Y. Liu, and W. Duan, Thermal engineering in low-dimensional quantum devices: A tutorial review of nonequilibrium Green’s function methods, Small Methods 2(6), 1700343 (2018)
https://doi.org/10.1002/smtd.201700343
5 D. G. Cahill, P. V. Braun, G. Chen, D. R. Clarke, S. Fan, K. E. Goodson, P. Keblinski, W. P. King, G. D. Mahan, A. Majumdar, H. J. Maris, S. R. Phillpot, E. Pop, and L. Shi, Nanoscale thermal transport (II): 2003–2012, Appl. Phys. Rev. 1(1), 011305 (2014)
https://doi.org/10.1063/1.4832615
6 B. Li, L. Wang, and G. Casati, Thermal diode: Rectification of heat flux, Phys. Rev. Lett. 93(18), 184301 (2004)
https://doi.org/10.1103/PhysRevLett.93.184301
7 B. Li, L. Wang, and G. Casati, Negative differential thermal resistance and thermal transistor, Appl. Phys. Lett. 88(14), 143501 (2006)
https://doi.org/10.1063/1.2191730
8 W. Chung Lo, L. Wang, and B. Li, Thermal Transistor: Heat Flux Switching and Modulating, J. Phys. Soc. Jpn. 77(5), 054402 (2008)
https://doi.org/10.1143/JPSJ.77.054402
9 L. Wang and B. Li, Thermal logic gates: Computation with phonons, Phys. Rev. Lett. 99(17), 177208 (2007)
https://doi.org/10.1103/PhysRevLett.99.177208
10 L. Wang and B. Li, Thermal memory: A storage of phononic information, Phys. Rev. Lett. 101(26), 267203 (2008)
https://doi.org/10.1103/PhysRevLett.101.267203
11 H. Zhu, J. Yi, M. Y. Li, J. Xiao, L. Zhang, C. W. Yang, R. A. Kaindl, L. J. Li, Y. Wang, and X. Zhang, Observation of chiral phonons, Science 359(6375), 579 (2018)
https://doi.org/10.1126/science.aar2711
12 J. Lu, C. Qiu, M. Ke, and Z. Liu, Valley vortex states in sonic crystals, Phys. Rev. Lett. 116(9), 093901 (2016)
https://doi.org/10.1103/PhysRevLett.116.093901
13 J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, and Z. Liu, Observation of topological valley transport of sound in sonic crystals, Nat. Phys. 13(4), 369 (2017)
https://doi.org/10.1038/nphys3999
14 Y. Liu, Y. Xu, S. C. Zhang, and W. Duan, Model for topological phononics and phonon diode, Phys. Rev. B 96(6), 064106 (2017)
https://doi.org/10.1103/PhysRevB.96.064106
15 S. Twaha, J. Zhu, Y. Yan, and B. Li, A comprehensive review of thermoelectric technology: Materials, applications, modelling and performance improvement, Renew. Sustain. Energy Rev. 65, 698 (2016)
https://doi.org/10.1016/j.rser.2016.07.034
16 D. Li, Y. Gong, Y. Chen, J. Lin, Q. Khan, Y. Zhang, Y. Li, H. Zhang, and H. Xie, Recent progress of twodimensional thermoelectric materials, Nano-Micro Lett. 12(1), 36 (2020)
https://doi.org/10.1007/s40820-020-0374-x
17 L. D. Zhao, S. H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid, and M. G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature 508(7496), 373 (2014)
https://doi.org/10.1038/nature13184
18 M. J. Lee, J. H. Ahn, J. H. Sung, H. Heo, S. G. Jeon, W. Lee, J. Y. Song, K. H. Hong, B. Choi, S. H. Lee, and M. H. Jo, Thermoelectric materials by using two-dimensional materials with negative correlation between electrical and thermal conductivity, Nat. Commun. 7(1), 12011 (2016)
https://doi.org/10.1038/ncomms12011
19 C. Chang, M. Wu, D. He, Y. Pei, C. F. Wu, X. Wu, H. Yu, F. Zhu, K. Wang, Y. Chen, L. Huang, J. F. Li, J. He, and L. D. Zhao, 3D charge and 2D phonon transports leading to high out-of-plane ZTin n-type SnSe crystals, Science 360(6390), 778 (2018)
https://doi.org/10.1126/science.aaq1479
20 H. Babaei, J. M. Khodadadi, and S. Sinha, Large theoretical thermoelectric power factor of suspended single-layer MoS2, Appl. Phys. Lett. 105(19), 193901 (2014)
https://doi.org/10.1063/1.4901342
21 C. Caroli, R. Combescot, P. Nozieres, and D. Saint-James, Direct calculation of the tunneling current, J. Phys. C 4(8), 916 (1971)
https://doi.org/10.1088/0022-3719/4/8/018
22 Y. Meir, and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett. 68(16), 2512 (1992)
https://doi.org/10.1103/PhysRevLett.68.2512
23 A. P. Jauho, N. S. Wingreen, and Y. Meir, Timedependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50(8), 5528 (1994)
https://doi.org/10.1103/PhysRevB.50.5528
24 J. S. Wang, J. Wang, and N. Zeng, Nonequilibrium Green’s function approach to mesoscopic thermal transport, Phys. Rev. B 74(3), 033408 (2006)
https://doi.org/10.1103/PhysRevB.74.033408
25 J. S. Wang, N. Zeng, J. Wang, and C. K. Gan, Nonequilibrium Green’s function method for thermal transport in junctions, Phys. Rev. E 75(6), 061128 (2007)
https://doi.org/10.1103/PhysRevE.75.061128
26 N. Sergueev, D. Roubtsov, and H. Guo, Ab initioanalysis of electron–phonon coupling in molecular devices, Phys. Rev. Lett. 95(14), 146803 (2005)
https://doi.org/10.1103/PhysRevLett.95.146803
27 T. Shimazaki and Y. Asai, Bias voltage dependence on the vibronic electric current, Phys. Rev. B 77(7), 075110 (2008)
https://doi.org/10.1103/PhysRevB.77.075110
28 M. Paulsson, T. Frederiksen, and M. Brandbyge, Modeling inelastic phonon scattering in atomic- and molecularwire junctions, Phys. Rev. B 72(20), 201101 (2005)
https://doi.org/10.1103/PhysRevB.72.201101
29 A. Ferretti, A. Calzolari, R. Di Felice, F. Manghi, M. J. Caldas, M. B. Nardelli, and E. Molinari, First-principles theory of correlated transport through nanojunctions, Phys. Rev. Lett. 94(11), 116802 (2005)
https://doi.org/10.1103/PhysRevLett.94.116802
30 K. S. Thygesen and A. Rubio, Conserving GW scheme for nonequilibrium quantum transport in molecular contacts, Phys. Rev. B 77(11), 115333 (2008)
https://doi.org/10.1103/PhysRevB.77.115333
31 J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B 63(24), 245407 (2001)
https://doi.org/10.1103/PhysRevB.63.245407
32 M. Brandbyge, J. L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Density-functional method for nonequilibrium electron transport, Phys. Rev. B 65(16), 165401 (2002)
https://doi.org/10.1103/PhysRevB.65.165401
33 Z. Y. Ong and E. Pop, Effect of substrate modes on thermal transport in supported graphene, Phys. Rev. B 84(7), 075471 (2011)
https://doi.org/10.1103/PhysRevB.84.075471
34 G. Zhang and B. Li, Thermal conductivity of nanotubes revisited: Effects of chirality, isotope impurity, tube length, and temperature, J. Chem. Phys. 123(11), 114714 (2005)
https://doi.org/10.1063/1.2036967
35 G. Zhang and H. Zhang, Thermal conduction and rectification in few-layer graphene Y junctions, Nanoscale 3(11), 4604 (2011)
https://doi.org/10.1039/c1nr10945f
36 R. Yang and G. Chen, Thermal conductivity modeling of periodic two-dimensional nanocomposites, Phys. Rev. B 69(19), 195316 (2004)
https://doi.org/10.1103/PhysRevB.69.195316
37 W. Li, N. Mingo, L. Lindsay, D. A. Broido, D. A. Stewart, and N. A. Katcho, Thermal conductivity of diamond nanowires from first principles, Phys. Rev. B 85(19), 195436 (2012)
https://doi.org/10.1103/PhysRevB.85.195436
38 W. Li, J. Carrete, N. A. Katcho, and N. Mingo, Sheng-BTE: A solver of the Boltzmann transport equation for phonons, Comput. Phys. Commun. 185(6), 1747 (2014)
https://doi.org/10.1016/j.cpc.2014.02.015
39 J. S. Wang, J. Wang, and J. T. Lü, Quantum thermal transport in nanostructures, Eur. Phys. J. B 62(4), 381 (2008)
https://doi.org/10.1140/epjb/e2008-00195-8
40 J.-S. Wang, B. K. Agarwalla, H. Li, and J. Thingna, Nonequilibrium Green’s function method for quantum thermal transport, Front. Phys. 9(6), 673 (2014)
https://doi.org/10.1007/s11467-013-0340-x
41 H. Haug and A. P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer-Verlag, Berlin, 1998
42 N. Mingo and L. Yang, Phonon transport in nanowires coated with an amorphous material: An atomistic Green’s function approach, Phys. Rev. B 68(24), 245406 (2003)
https://doi.org/10.1103/PhysRevB.68.245406
43 T. Yamamoto and K. Watanabe, Nonequilibrium Green’s function approach to phonon transport in defective carbon nanotubes, Phys. Rev. Lett. 96(25), 255503 (2006)
https://doi.org/10.1103/PhysRevLett.96.255503
44 L. Zhang, J. Thingna, D. He, J. S. Wang, and B. Li, Nonlinearity enhanced interfacial thermal conductance and rectification, EPL (Europhys. Lett.) 103(6), 64002 (2013)
https://doi.org/10.1209/0295-5075/103/64002
45 J. T. Lü and J. S. Wang, Coupled electron and phonon transport in one-dimensional atomic junctions, Phys. Rev. B 76(16), 165418 (2007)
https://doi.org/10.1103/PhysRevB.76.165418
46 L. Zhang, J. T. Lü, J. S. Wang, and B. Li, Thermal transport across metal–insulator interface via electron–phonon interaction, J. Phys.: Condens. Matter 25(44), 445801 (2013)
https://doi.org/10.1088/0953-8984/25/44/445801
47 K. Gordiz and A. Henry, Examining the effects of stiffness and mass difference on the thermal interface conductance between Lennard–Jones solids, Sci. Rep. 5(1), 18361 (2015)
https://doi.org/10.1038/srep18361
48 J. Chen, J. H. Walther, and P. Koumoutsakos, Covalently bonded graphene–carbon nanotube hybrid for high-performance thermal interfaces, Adv. Funct. Mater. 25(48), 7539 (2015)
https://doi.org/10.1002/adfm.201501593
49 W. A. Little, The transport of heat between dissimilar solids at low temperatures, Can. J. Phys. 37(3), 334 (1959)
https://doi.org/10.1139/p59-037
50 E. T. Swartz and R. O. Pohl, Thermal boundary resistance, Rev. Mod. Phys. 61(3), 605 (1989)
https://doi.org/10.1103/RevModPhys.61.605
51 L. Zhang, P. Keblinski, J. S. Wang, and B. Li, Interfacial thermal transport in atomic junctions, Phys. Rev. B Condens. Matter Mater. Phys. 83(6), 064303 (2011)
https://doi.org/10.1103/PhysRevB.83.064303
52 C. B. Saltonstall, C. A. Polanco, J. C. Duda, A. W. Ghosh, P. M. Norris, and P. E. Hopkins, Effect of interface adhesion and impurity mass on phonon transport at atomic junctions, J. Appl. Phys. 113(1), 013516 (2013)
https://doi.org/10.1063/1.4773331
53 G. Xiong, J. S. Wang, D. Ma, and L. Zhang, Dramatic enhancement of interfacial thermal transport by massgraded and coupling-graded materials, EPL (Europhys. Lett.) 128(5), 54007 (2020)
https://doi.org/10.1209/0295-5075/128/54007
54 B. Chen and L. Zhang, Optimized couplers for interfacial thermal transport, J. Phys.: Condens. Matter 27(12), 125401 (2015)
https://doi.org/10.1088/0953-8984/27/12/125401
55 D. He, J. Thingna, J. S. Wang, and B. Li, Quantum thermal transport through anharmonic systems: A selfconsistent approach, Phys. Rev. B 94(15), 155411 (2016)
https://doi.org/10.1103/PhysRevB.94.155411
56 J. Fang, X. Qian, C. Y. Zhao, B. Li, and X. Gu, Monitoring anharmonic phonon transport across interfaces in one-dimensional lattice chains, Phys. Rev. E 101(2), 022133 (2020)
https://doi.org/10.1103/PhysRevE.101.022133
57 J. C. Klöckner, M. Bürkle, J. C. Cuevas, and F. Pauly, Length dependence of the thermal conductance of alkanebased single-molecule junctions: An ab initio study, Phys. Rev. B 94(20), 205425 (2016)
https://doi.org/10.1103/PhysRevB.94.205425
58 J. C. Klöckner, R. Siebler, J. C. Cuevas, and F. Pauly, Thermal conductance and thermoelectric figure of merit of C60-based single-molecule junctions: Electrons, phonons, and photons, Phys. Rev. B 95(24), 245404 (2017)
https://doi.org/10.1103/PhysRevB.95.245404
59 L. Cui, R. Miao, C. Jiang, E. Meyhofer, and P. Reddy, Perspective: Thermal and thermoelectric transport in molecular junctions, J. Chem. Phys. 146(9), 092201 (2017)
https://doi.org/10.1063/1.4976982
60 L. Hu, L. Zhang, M. Hu, J. S. Wang, B. Li, and P. Keblinski, Phonon interference at self-assembled monolayer interfaces: Molecular dynamics simulations, Phys. Rev. B 81(23), 235427 (2010)
https://doi.org/10.1103/PhysRevB.81.235427
61 J. Lu, K. Yuan, F. Sun, K. Zheng, Z. Zhang, J. Zhu, X. Wang, X. Zhang, Y. Zhuang, Y. Ma, X. Cao, J. Zhang, and D. Tang, Self-assembled monolayers for the polymer/semiconductor interface with improved interfacial thermal management, ACS Appl. Mater. Interfaces 11(45), 42708 (2019)
https://doi.org/10.1021/acsami.9b12006
62 H. Fan, M. Wang, D. Han, J. Zhang, J. Zhang, and X. Wang, Enhancement of interfacial thermal transport between metal and organic semiconductor using selfassembled monolayers with different terminal groups, J. Phys. Chem. C 124(31), 16748 (2020)
https://doi.org/10.1021/acs.jpcc.0c02753
63 X. Chen, Y. Xu, X. Zou, B. L. Gu, and W. Duan, Interfacial thermal conductance of partially unzipped carbon nanotubes: Linear scaling and exponential decay, Phys. Rev. B 87(15), 155438 (2013)
https://doi.org/10.1103/PhysRevB.87.155438
64 W. Zhang, N. Mingo, and T. S. Fisher, Simulation of phonon transport across a non-polar nanowire junction using an atomistic Green’s function method, Phys. Rev. B 76(19), 195429 (2007)
https://doi.org/10.1103/PhysRevB.76.195429
65 Y. Xu, X. Chen, B. L. Gu, and W. Duan, Intrinsic anisotropy of thermal conductance in graphene nanoribbons, Appl. Phys. Lett. 95(23), 233116 (2009)
https://doi.org/10.1063/1.3272678
66 Y. Xu, X. Chen, J. S. Wang, B. L. Gu, and W. Duan, Thermal transport in graphene junctions and quantum dots, Phys. Rev. B 81(19), 195425 (2010)
https://doi.org/10.1103/PhysRevB.81.195425
67 Z. Ding, Q. X. Pei, J. W. Jiang, W. Huang, and Y. W. Zhang, Interfacial thermal conductance in graphene/MoS2 heterostructures, Carbon 96, 888 (2016)
https://doi.org/10.1016/j.carbon.2015.10.046
68 S. Sadasivam, N. Ye, J. P. Feser, J. Charles, K. Miao, T. Kubis, and T. S. Fisher, Thermal transport across metal silicide-silicon interfaces: First-principles calculations and Green’s function transport simulations, Phys. Rev. B 95(8), 085310 (2017)
https://doi.org/10.1103/PhysRevB.95.085310
69 Z. Zhang, Y. Xie, Q. Peng, and Y. Chen, Phonon transport in single-layer boron nanoribbons, Nanotechnology 27(44), 445703 (2016)
https://doi.org/10.1088/0957-4484/27/44/445703
70 Y. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336(1–2), 1 (2000)
https://doi.org/10.1016/S0370-1573(99)00123-4
71 M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57(14), 1761 (1986)
https://doi.org/10.1103/PhysRevLett.57.1761
72 M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38(14), 9375 (1988)
https://doi.org/10.1103/PhysRevB.38.9375
73 L. Zhang, J. S. Wang, and B. Li, Ballistic thermal rectification in nanoscale three-terminal junctions, Phys. Rev. B 81(10), 100301 (2010)
https://doi.org/10.1103/PhysRevB.81.100301
74 Y. Ming, Z. X. Wang, Z. J. Ding, and H. M. Li, Ballistic thermal rectification in asymmetric three-terminal mesoscopic dielectric systems, New J. Phys. 12(10), 103041 (2010)
https://doi.org/10.1088/1367-2630/12/10/103041
75 T. Ouyang, Y. Chen, Y. Xie, X. L. Wei, K. Yang, P. Yang, and J. Zhong, Ballistic thermal rectification in asymmetric three-terminal graphene nanojunctions, Phys. Rev. B 82(24), 245403 (2010)
https://doi.org/10.1103/PhysRevB.82.245403
76 Z. X. Xie, K. M. Li, L. M. Tang, C. N. Pan, and K. Q. Chen, Nonlinear phonon transport and ballistic thermal rectification in asymmetric graphene-based three terminal junctions, Appl. Phys. Lett. 100(18), 183110 (2012)
https://doi.org/10.1063/1.4711204
77 Y. Gu, Mode-dependent phonon transmission in a Tshaped three-terminal graphene nanojunction, Carbon 158, 818 (2020)
https://doi.org/10.1016/j.carbon.2019.11.059
78 L. Zhang, J. S. Wang, and B. Li, Phonon Hall effect in four-terminal nano-junctions, New J. Phys. 11(11), 113038 (2009)
https://doi.org/10.1088/1367-2630/11/11/113038
79 Y. Xing, Q. F. Sun, and J. Wang, Nature of spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin–orbit interaction, Phys. Rev. B 73(20), 205339 (2006)
https://doi.org/10.1103/PhysRevB.73.205339
80 Y. Xing, Q. F. Sun, and J. Wang, Symmetry and transport property of spin current induced spin-Hall effect, Phys. Rev. B 75(7), 075324 (2007)
https://doi.org/10.1103/PhysRevB.75.075324
81 M. Wei, M. Zhou, B. Wang, and Y. Xing, Thermoelectric transport properties of ferromagnetic graphene with CTinvariant quantum spin Hall effect, Phys. Rev. B 102(7), 075432 (2020)
https://doi.org/10.1103/PhysRevB.102.075432
82 C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phenomenological evidence for the phonon Hall effect, Phys. Rev. Lett. 95(15), 155901 (2005)
https://doi.org/10.1103/PhysRevLett.95.155901
83 E. C. Cuansing and J. S. Wang, Transient behavior of heat transport in a thermal switch, Phys. Rev. B 81(5), 052302 (2010)
https://doi.org/10.1103/PhysRevB.81.052302
84 R. Tuovinen, N. Säkkinen, D. Karlsson, G. Stefanucci, and R. van Leeuwen, Phononic heat transport in the transient regime: An analytic solution, Phys. Rev. B 93(21), 214301 (2016)
https://doi.org/10.1103/PhysRevB.93.214301
85 E. C. Cuansing and J. S. Wang, Erratum: Transient behavior of heat transport in a thermal switch [Phys. Rev. B 81, 052302 (2010)], Phys. Rev. B 83(1), 019902 (2011)
https://doi.org/10.1103/PhysRevB.83.019902
86 J. S. Wang, B. K. Agarwalla, and H. Li, Transient behavior of full counting statistics in thermal transport, Phys. Rev. B 84(15), 153412 (2011)
https://doi.org/10.1103/PhysRevB.84.153412
87 B. K. Agarwalla, B. Li, and J. S. Wang, Full-counting statistics of heat transport in harmonic junctions: Transient, steady states, and fluctuation theorems, Phys. Rev. E. 85(5), 051142 (2012)
https://doi.org/10.1103/PhysRevE.85.051142
88 B. K. Agarwalla, J. H. Jiang, and D. Segal, Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency, Phys. Rev. B 92(24), 245418 (2015)
https://doi.org/10.1103/PhysRevB.92.245418
89 K. Saito and A. Dhar, Fluctuation theorem in quantum heat conduction, Phys. Rev. Lett. 99(18), 180601 (2007)
https://doi.org/10.1103/PhysRevLett.99.180601
90 K. Saito and A. Dhar, Generating function formula of heat transfer in harmonic networks, Phys. Rev. E 83(4), 041121 (2011)
https://doi.org/10.1103/PhysRevE.83.041121
91 Y. Dubi and M. Di Ventra, Heat flow and thermoelectricity in atomic and molecular junctions, Rev. Mod. Phys. 83(1), 131 (2011)
https://doi.org/10.1103/RevModPhys.83.131
92 A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature 451(7175), 163 (2008)
https://doi.org/10.1038/nature06381
93 P. Reddy, S. Y. Jang, R. A. Segalman, and A. Majumdar, Thermoelectricity in molecular junctions, Science 315(5818), 1568 (2007)
https://doi.org/10.1126/science.1137149
94 T. Gunst, T. Markussen, A. P. Jauho, and M. Brandbyge, Thermoelectric properties of finite graphene antidot lattices, Phys. Rev. B 84(15), 155449 (2011)
https://doi.org/10.1103/PhysRevB.84.155449
95 Y. Chen, T. Jayasekera, A. Calzolari, K. W. Kim, and M. B. Nardelli, Thermoelectric properties of graphene nanoribbons, junctions and superlattices, J. Phys.: Condens. Matter 22(37), 372202 (2010)
https://doi.org/10.1088/0953-8984/22/37/372202
96 K. Yang, Y. Chen, R. D’Agosta, Y. Xie, J. Zhong, and A. Rubio, Enhanced thermoelectric properties in hybrid graphene/boron nitride nanoribbons, Phys. Rev. B 86(4), 045425 (2012)
https://doi.org/10.1103/PhysRevB.86.045425
97 Y. Xing, Q. F. Sun, and J. Wang, Nernst and Seebeck effects in a graphene nanoribbon, Phys. Rev. B 80(23), 235411 (2009)
https://doi.org/10.1103/PhysRevB.80.235411
98 M. M. Wei, Y. T. Zhang, A. M. Guo, J. J. Liu, Y. Xing, and Q. F. Sun, Magnetothermoelectric transport properties of multiterminal graphene nanoribbons, Phys. Rev. B 93(24), 245432 (2016)
https://doi.org/10.1103/PhysRevB.93.245432
99 B. Wang, J. Zhou, R. Yang, and B. Li, Ballistic thermoelectric transport in structured nanowires, New J. Phys. 16(6), 065018 (2014)
https://doi.org/10.1088/1367-2630/16/6/065018
100 J. Li, B. Wang, F. Xu, Y. Wei, and J. Wang, Spindependent Seebeck effects in graphene-based molecular junctions, Phys. Rev. B 93(19), 195426 (2016)
https://doi.org/10.1103/PhysRevB.93.195426
101 B. Zhou, B. Zhou, Y. Yao, G. Zhou, and M. Hu, Spindependent Seebeck effects in a graphene superlattice p–n junction with different shapes, J. Phys.: Condens. Matter 29(40), 405303 (2017)
https://doi.org/10.1088/1361-648X/aa80cc
102 P. N. Butcher, Thermal and electrical transport formalism for electronic microstructures with many terminals, J. Phys.: Condens. Matter 2(22), 4869 (1990)
https://doi.org/10.1088/0953-8984/2/22/008
103 U. Sivan and Y. Imry, Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge, Phys. Rev. B 33(1), 551 (1986)
https://doi.org/10.1103/PhysRevB.33.551
104 G. D. Mahan, Many-Particle Physics, Springer, New York, 2000
https://doi.org/10.1007/978-1-4757-5714-9
105 J. Ren, J. X. Zhu, J. E. Gubernatis, C. Wang, and B. Li, Thermoelectric transport with electron–phonon coupling and electron–electron interaction in molecular junctions, Phys. Rev. B85(15), 155443 (2012)
https://doi.org/10.1103/PhysRevB.85.155443
106 K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, Nature 455(7214), 778 (2008)
https://doi.org/10.1038/nature07321
107 G. E. Bauer, A. H. MacDonald, and S. Maekawa, Spin caloritronics, Solid State Commun. 150(11–12), 459 (2010)
https://doi.org/10.1016/j.ssc.2010.01.022
108 G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11(5), 391 (2012)
https://doi.org/10.1038/nmat3301
109 M. Hatami, G. E. W. Bauer, Q. Zhang, and P. J. Kelly, Thermal spin-transfer torque in magnetoelectronic devices, Phys. Rev. Lett. 99(6), 066603 (2007)
https://doi.org/10.1103/PhysRevLett.99.066603
110 Z. Zhang, L. Bai, X. Chen, H. Guo, X. L. Fan, D. S. Xue, D. Houssameddine, and C. M. Hu, Observation of thermal spin-transfer torque via ferromagnetic resonance in magnetic tunnel junctions, Phys. Rev. B 94(6), 064414 (2016)
https://doi.org/10.1103/PhysRevB.94.064414
111 M. Zeng, Y. Feng, and G. Liang, Graphene-based spin caloritronics, Nano Lett. 11(3), 1369 (2011)
https://doi.org/10.1021/nl2000049
112 X. Q. Yu, Z. G. Zhu, G. Su, and A. P. Jauho, Thermally driven pure spin and valley currents via the anomalous nernst effect in monolayer Group-VI dichalcogenides, Phys. Rev. Lett. 115(24), 246601 (2015)
https://doi.org/10.1103/PhysRevLett.115.246601
113 S. G. Cheng, Y. Xing, Q. F. Sun, and X. C. Xie, Spin Nernst effect and Nernst effect in two-dimensional electron systems, Phys. Rev. B78(4), 045302 (2008)
https://doi.org/10.1103/PhysRevB.78.045302
114 Q. Wang, J. Li, Y. Nie, F. Xu, Y. Yu, and B. Wang, Pure spin current and phonon thermoelectric transport in a triangulene-based molecular junction, Phys. Chem. Chem. Phys. 20(23), 15736 (2018)
https://doi.org/10.1039/C8CP02322K
115 D. Xiao, W. Yao, and Q. Niu, Valley-contrasting physics in graphene: Magnetic moment and topological transport, Phys. Rev. Lett. 99(23), 236809 (2007)
https://doi.org/10.1103/PhysRevLett.99.236809
116 C. E. Nebel, Electrons dance in diamond, Nat. Mater. 12(8), 690 (2013)
https://doi.org/10.1038/nmat3724
117 A. Rycerz, J. Tworzydlo, and C. W. J. Beenakker, Valley filter and valley valve in graphene, Nat. Phys. 3(3), 172 (2007)
https://doi.org/10.1038/nphys547
118 D. Gunlycke and C. T. White, Graphene valley filter using a line defect, Phys. Rev. Lett. 106(13), 136806 (2011)
https://doi.org/10.1103/PhysRevLett.106.136806
119 Y. Jiang, T. Low, K. Chang, M. I. Katsnelson, and F. Guinea, Generation of pure bulk valley current in graphene, Phys. Rev. Lett. 110(4), 046601 (2013)
https://doi.org/10.1103/PhysRevLett.110.046601
120 Z. Yu, F. Xu, and J. Wang, Valley Seebeck effect in gate tunable zigzag graphene nanoribbons, Carbon 99, 451 (2016)
https://doi.org/10.1016/j.carbon.2015.12.033
121 L. Zhang, Z. Yu, F. Xu, and J. Wang, Influence of dephasing and B/N doping on valley Seebeck effect in zigzag graphene nanoribbons, Carbon 126, 183 (2018)
https://doi.org/10.1016/j.carbon.2017.10.017
122 X. Chen, L. Zhang, and H. Guo, Valley caloritronics and its realization by graphene nanoribbons, Phys. Rev. B 92(15), 155427 (2015)
https://doi.org/10.1103/PhysRevB.92.155427
123 X. Zhai, W. Gao, X. Cai, D. Fan, Z. Yang, and L. Meng, Spin-valley caloritronics in silicene near room temperature, Phys. Rev. B 94(24), 245405 (2016)
https://doi.org/10.1103/PhysRevB.94.245405
124 Z. P. Niu and S. Dong, Valley and spin thermoelectric transport in ferromagnetic silicene junctions, Appl. Phys. Lett. 104(20), 202401 (2014)
https://doi.org/10.1063/1.4876927
125 X. Zhai, S. Wang, and Y. Zhang, Valley–spin Seebeck effect in heavy group-IV monolayers, New J. Phys. 19(6), 063007 (2017)
https://doi.org/10.1088/1367-2630/aa6d37
126 G. Stefanucci and C. O. Almbladh, Time-dependent partition-free approach in resonant tunneling systems, Phys. Rev. B 69(19), 195318 (2004)
https://doi.org/10.1103/PhysRevB.69.195318
127 M. Cini, Time-dependent approach to electron transport through junctions: General theory and simple applications, Phys. Rev. B 22(12), 5887 (1980)
https://doi.org/10.1103/PhysRevB.22.5887
128 C. Caroli, R. Combescot, D. Lederer, P. Nozieres, and D. Saint-James, A direct calculation of the tunnelling current (II): Free electron description, J. Phys. C 4(16), 2598 (1971)
https://doi.org/10.1088/0022-3719/4/16/025
129 Z. Yu, J. Yuan, and J. Wang, Time-dependent thermoelectric transport in mesoscopic systems under a quantum quench, Phys. Rev. B 101(23), 235433 (2020)
https://doi.org/10.1103/PhysRevB.101.235433
130 B. Wang, J. Wang, and H. Guo, Current partition: A nonequilibrium Green’s function approach, Phys. Rev. Lett. 82(2), 398 (1999)
https://doi.org/10.1103/PhysRevLett.82.398
131 J. Chen, M. ShangGuan, and J. Wang, A gauge invariant theory for time dependent heat current, New J. Phys. 17(5), 053034 (2015)
https://doi.org/10.1088/1367-2630/17/5/053034
132 X. Chen, J. Yuan, G. Tang, J. Wang, Z. Zhang, C. M. Hu, and H. Guo, Transient spin current under a thermal switch, J. Phys. D 51(27), 274004 (2018)
https://doi.org/10.1088/1361-6463/aac7ca
133 F. G. Eich, A. Principi, M. Di Ventra, and G. Vignale, Luttinger-field approach to thermoelectric transport in nanoscale conductors, Phys. Rev. B 90(11), 115116 (2014)
https://doi.org/10.1103/PhysRevB.90.115116
134 F. G. Eich, M. Di Ventra, and G. Vignale, Temperaturedriven transient charge and heat currents in nanoscale conductors, Phys. Rev. B 93(13), 134309 (2016)
https://doi.org/10.1103/PhysRevB.93.134309
135 Č. Lozej and T. Rejec, Time-dependent thermoelectric transport in nanosystems: Reflectionless Luttinger field approach, Phys. Rev. B 98(7), 075427 (2018)
https://doi.org/10.1103/PhysRevB.98.075427
136 A. Crépieux, F. Šimkovic, B. Cambon, and F. Michelini, Enhanced thermopower under a time-dependent gate voltage, Phys. Rev. B 83(15), 153417 (2011)
https://doi.org/10.1103/PhysRevB.83.153417
137 A. Kara Slimane, P. Reck, and G. Fleury, Simulating time-dependent thermoelectric transport in quantum systems, Phys. Rev. B 101(23), 235413 (2020)
https://doi.org/10.1103/PhysRevB.101.235413
138 M. M. Odashima and C. H. Lewenkopf, Time-dependent resonant tunneling transport: Keldysh and Kadanoff-Baym nonequilibrium Green’s functions in an analytically soluble problem, Phys. Rev. B 95(10), 104301 (2017)
https://doi.org/10.1103/PhysRevB.95.104301
139 M. Ridley, and R. Tuovinen, Formal equivalence between partitioned and partition-free quenches in quantum transport, J. Low Temp. Phys. 191(5–6), 380 (2018)
https://doi.org/10.1007/s10909-018-1880-9
140 A. M. Daré and P. Lombardo, Time-dependent thermoelectric transport for nanoscale thermal machines, Phys. Rev. B 93(3), 035303 (2016)
https://doi.org/10.1103/PhysRevB.93.035303
141 Z. Yu, L. Zhang, Y. Xing, and J. Wang, Investigation of transient heat current from first principles using complex absorbing potential, Phys. Rev. B 90(11), 115428 (2014)
https://doi.org/10.1103/PhysRevB.90.115428
142 Z. Yu, G. M. Tang, and J. Wang, Full-counting statistics of transient energy current in mesoscopic systems, Phys. Rev. B 93(19), 195419 (2016)
https://doi.org/10.1103/PhysRevB.93.195419
143 H. Li, B. K. Agarwalla, and J. S. Wang, Cumulant generating function formula of heat transfer in ballistic systems with lead-lead coupling, Phys. Rev. B 86(16), 165425 (2012)
https://doi.org/10.1103/PhysRevB.86.165425
144 M. Ridley, M. Galperin, E. Gull, and G. Cohen, Numerically exact full counting statistics of the energy current in the Kondo regime, Phys. Rev. B 100(16), 165127 (2019)
https://doi.org/10.1103/PhysRevB.100.165127
145 G. Tang, J. Thingna, and J. Wang, Thermodynamics of energy, charge, and spin currents in a thermoelectric quantum-dot spin valve, Phys. Rev. B 97(15), 155430 (2018)
https://doi.org/10.1103/PhysRevB.97.155430
146 G. Tang, X. Chen, J. Ren, and J. Wang, Rectifying fullcounting statistics in a spin Seebeck engine, Phys. Rev. B 97(8), 081407 (2018)
https://doi.org/10.1103/PhysRevB.97.081407
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed