Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2014, Vol. 9 Issue (6) : 698-710    https://doi.org/10.1007/s11467-013-0361-5
REVIEW ARTICLE
Time-dependent density functional theory for quantum transport
Yanho Kwok,Yu Zhang,GuanHua Chen()
Department of Chemistry, The University of Hong Kong, Hong Kong, China
 Download: PDF(1130 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The rapid miniaturization of electronic devices motivates research interests in quantum transport. Recently time-dependent quantum transport has become an important research topic. Here we review recent progresses in the development of time-dependent density-functional theory for quantum transport including the theoretical foundation and numerical algorithms. In particular, the reducedsingle electron density matrix based hierarchical equation of motion, which can be derived from Liouville–von Neumann equation, is reviewed in details. The numerical implementation is discussed and simulation results of realistic devices will be given.

Keywords tim-dependent density functional theory (TDDFT)      quantum transport      nonequilibrium Green’s function     
Corresponding Author(s): GuanHua Chen   
Issue Date: 24 December 2014
 Cite this article:   
Yanho Kwok,Yu Zhang,GuanHua Chen. Time-dependent density functional theory for quantum transport[J]. Front. Phys. , 2014, 9(6): 698-710.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-013-0361-5
https://academic.hep.com.cn/fop/EN/Y2014/V9/I6/698
1 M. Auf der Maur, M. Povolotskyi, F. Sacconi, A. Pecchia, G. Romano, G. Penazzi, and A. Di Carlo, TiberCAD: Towards multiscale simulation of optoelectronic devices, Opt. Quantum Electron., 2008, 40(14-15): 1077
https://doi.org/10.1007/s11082-009-9272-7
2 M. C. Petty, Molecular Electronics: From Principles to Practice, Wiley, 2008: 544
3 A. Aviram and M. A. Ratner, Molecular rectifiers, Chem. Phys. Lett., 1974, 29(2): 277
https://doi.org/10.1016/0009-2614(74)85031-1
4 M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Conductance of a molecular junction, Science, 1997, 278(5336): 252
https://doi.org/10.1126/science.278.5336.252
5 H. Song, Y. Kim, Y. H. Jang, H. Jeong, M. A. Reed, and T. Lee, Observation of molecular orbital gating, Nature, 2009, 462(7276): 1039
https://doi.org/10.1038/nature08639
6 H. Song, M. A. Reed, and T. Lee, Single molecule electronic devices, Adv. Mater., 2011, 23(14): 1583
https://doi.org/10.1002/adma.201004291
7 S. W. Wu, N. Ogawa, and W. Ho, Atomic-scale coupling of photons to single-molecule junctions, Science, 2006, 312(5778): 1362
https://doi.org/10.1126/science.1124881
8 M. Galperin, and A. Nitzan, Molecular optoelectronics: the interaction of molecular conduction junctions with light, Phys. Chem. Chem. Phys., 2012, 14(26): 9421
https://doi.org/10.1039/c2cp40636e
9 A. Nitzan and M. A. Ratner, Electron transport in molecular wire junctions, Science, 2003, 300(5624): 1384
https://doi.org/10.1126/science.1081572
10 M. Paulsson, T. Frederiksen, and M. Brandbyge, Inelastic transport through molecules: Comparing first-principles calculations to experiments, Nano Lett., 2006, 6(2): 258
https://doi.org/10.1021/nl052224r
11 M. Galperin, M. A Ratner, and A. Nitzan, Molecular transport junctions: Vibrational effects, J. Phys.: Condens. Matter, 2007, 19(10): 103201
https://doi.org/10.1088/0953-8984/19/10/103201
12 J. C. Cuevas and E. Scheer, Molecular Electronics: An Introduction to Theory and Experiment, Vol. 1, World Scientific Series in Nanotechnology and Nanoscience, 2010: 703
https://doi.org/10.1142/7434
13 T. Fujisawa, D. G. Austing, Y. Tokura, Y. Hirayama, and S. Tarucha, Electrical pulse measurement, inelastic relaxation, and non-equilibrium transport in a quantum dot, J. Phys.: Condens. Matter, 2003, 15: R1395
https://doi.org/10.1088/0953-8984/15/33/201
14 J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B, 2001, 63(24): 245407
https://doi.org/10.1103/PhysRevB.63.245407
15 M. Brandbyge, J. L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Density-functional method for nonequilibrium electron transport, Phys. Rev. B, 2002, 65(16): 165401
https://doi.org/10.1103/PhysRevB.65.165401
16 M. Elstner, D. Porezag, G. Jungnickel, J. Elsner, M. Haugk, T. Frauenheim, S. Suhai, and G. Seifert, Self-consistentcharge density-functional tight-binding method for simulations of complex materials properties, Phys. Rev. B, 1998, 58(11): 7260
https://doi.org/10.1103/PhysRevB.58.7260
17 T. A. Niehaus, S. Suhai, F. Della Sala, P. Lugli, M. Elstner, G. Seifert, and T. Frauenheim, Tight-binding approach to time-dependent density-functional response theory, Phys. Rev. B, 2001, 63(8): 085108
https://doi.org/10.1103/PhysRevB.63.085108
18 C. Yam, L. Meng, G. H. Chen, Q. Chen, and N. Wong, Multiscale quantum mechanics/electromagnetics simulation for electronic devices, Phys. Chem. Chem. Phys., 2011, 13(32): 14365
https://doi.org/10.1039/c1cp20766k
19 L. Meng, C. Yam, S. Koo, Q. Chen, N. Wong, and G. H. Chen, Dynamic multiscale quantum mechanics/ electromagnetics simulation method, J. Chem. Theory Comput., 2012, 8(4): 1190
https://doi.org/10.1021/ct200859h
20 G. Stefanucci and C. O. Almbladh, Time-dependent quantum transport: An exact formulation based on TDDFT, Europhys. Lett., 2004, 67(1): 14
https://doi.org/10.1209/epl/i2004-10043-7
21 J. Maciejko, J. Wang, and H. Guo, Time-dependent quantum transport far from equilibrium: An exact nonlinear response theory, Phys. Rev. B, 2006, 74(8): 085324
https://doi.org/10.1103/PhysRevB.74.085324
22 S. Kurth, G. Stefanucci, C. O. Almbladh, A. Rubio, and E. K. U. Gross, Time-dependent quantum transport: A practical scheme using density functional theory, Phys. Rev. B, 2005, 72(3): 035308
https://doi.org/10.1103/PhysRevB.72.035308
23 J. Yuen-Zhou, D. G. Tempel, C. A. Rodríguez-Rosario, and A. Aspuru-Guzik, Time-dependent density functional theory for open quantum systems with unitary propagation, Phys. Rev. Lett., 2010, 104(4): 043001
https://doi.org/10.1103/PhysRevLett.104.043001
24 X. Zheng, F. Wang, C. Y. Yam, Y. Mo, and G. H. Chen, Time-dependent density-functional theory for open systems, Phys. Rev. B, 2007, 75(19): 195127
https://doi.org/10.1103/PhysRevB.75.195127
25 X. Zheng, G. H. Chen, Y. Mo, S. Koo, H. Tian, C. Yam, and Y. Yan, Time-dependent density functional theory for quantum transport, J. Chem. Phys., 2010, 133(11): 114101
https://doi.org/10.1063/1.3475566
26 S. H. Ke, R. Liu, W. Yang, and H. U. Baranger, Timedependent transport through molecular junctions, J. Chem. Phys., 2010, 132(23): 234105
https://doi.org/10.1063/1.3435351
27 K. Burke, R. Car, and R. Gebauer, Density functional theory of the electrical conductivity of molecular devices, Phys. Rev. Lett., 2005, 94(14): 146803
https://doi.org/10.1103/PhysRevLett.94.146803
28 Y. Zhang, S. Chen, and G. H. Chen, First-principles timedependent quantum transport theory, Phys. Rev. B, 2013, 87(8): 085110
https://doi.org/10.1103/PhysRevB.87.085110
29 S. Chen, H. Xie, Y. Zhang, X. Cui, and G. H. Chen, Quantum transport through an array of quantum dots, Nanoscale, 2013, 5(1): 169
https://doi.org/10.1039/c2nr32343e
30 A. P. Jauho, N. S. Wingreen, and Y. Meir, Timedependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B, 1994, 50(8): 5528
https://doi.org/10.1103/PhysRevB.50.5528
31 C. Y. Yam, Y. Mo, F. Wang, X. B. Li, G. H. Chen, X. Zheng, Y. Matsuda, J. Tahir-Kheli, and W. A. Goddard III, Dynamic admittance of carbon nanotube-based molecular electronic devices and their equivalent electric circuit, Nanotechnology, 2008, 19(49): 495203
https://doi.org/10.1088/0957-4484/19/49/495203
32 K. F. Albrecht, H. Wang, L. Mühlbacher, M. Thoss, and A. Komnik, Bistability signatures in nonequilibrium charge transport through molecular quantum dots, Phys. Rev. B, 2012, 86(8): 081412
https://doi.org/10.1103/PhysRevB.86.081412
33 E. Khosravi, S. Kurth, G. Stefanucci, and E. Gross, The role of bound states in time-dependent quantum transport, Appl. Phys. A, 2008, 93(2): 355
https://doi.org/10.1007/s00339-008-4864-9
34 E. Khosravi, G. Stefanucci, S. Kurth, and E. K. Gross, Bound states in time-dependent quantum transport: Oscillations and memory effects in current and density, Phys. Chem. Chem. Phys., 2009, 11(22): 4535
https://doi.org/10.1039/b906528h
35 B. Popescu, P. B. Woiczikowski, M. Elstner, and U. Kleinekath?fer, Time-dependent view of sequential transport through molecules with rapidly fluctuating bridges, Phys. Rev. Lett., 2012, 109(17): 176802
https://doi.org/10.1103/PhysRevLett.109.176802
36 J. K. Tomfohr and O. F. Sankey, Time-dependent simulation of conduction through a molecule, physica status solidi (b), 2001, 226(1): 115
37 N. Bushong, N. Sai, and M. Di Ventra, Approach to steadystate transport in nanoscale conductors, Nano Lett., 2005, 5(12): 2569
https://doi.org/10.1021/nl0520157
38 J. Muga, J. Palao, B. Navarro, and I. Egusquiza, Complex absorbing potentials, Phys. Rep., 2004, 395(6): 357
https://doi.org/10.1016/j.physrep.2004.03.002
39 R. Baer, T. Seideman, S. Ilani, and D. Neuhauser, Ab initio study of the alternating current impedance of a molecular junction, J. Chem. Phys., 2004, 120(7): 3387
https://doi.org/10.1063/1.1640611
40 P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev., 1964, 136(3B): B864
https://doi.org/10.1103/PhysRev.136.B864
41 E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett., 1984, 52(12): 997
https://doi.org/10.1103/PhysRevLett.52.997
42 S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. Ostergaard Sorensen, Analyticity of the density of electronic wavefunctions, Arkiv f?r Matematik, 2004, 42(1): 87
https://doi.org/10.1007/BF02432911
43 S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. Ostergaard Sorensen, The electron density is smooth away from the nuclei, Commun. Math. Phys., 2002, 228(3): 401
https://doi.org/10.1007/s002200200668
44 X. Zheng, C. Yam, F. Wang, and G. H. Chen, Existence of time-dependent density-functional theory for open electronic systems: Time-dependent holographic electron density theorem, Phys. Chem. Chem. Phys., 2011, 13(32): 14358
https://doi.org/10.1039/c1cp20777f
45 G. Vignale and W. Kohn, Current-dependent exchangecorrelation potential for dynamical linear response theory, Phys. Rev. Lett., 1996, 77(10): 2037
https://doi.org/10.1103/PhysRevLett.77.2037
46 M. Di Ventra and R. D’Agosta, Stochastic time-dependent current-density-functional theory, Phys. Rev. Lett., 2007, 98(22): 226403
https://doi.org/10.1103/PhysRevLett.98.226403
47 R. D’Agosta and M. Di Ventra, Stochastic time-dependent current-density-functional theory: A functional theory of open quantum systems, Phys. Rev. B, 2008, 78(16): 165105
https://doi.org/10.1103/PhysRevB.78.165105
48 M. Galperin and S. Tretiak, Linear optical response of current-carrying molecular junction: a nonequilibrium Green’s function-time-dependent density functional theory approach, J. Chem. Phys., 2008, 128(12): 124705
https://doi.org/10.1063/1.2876011
49 Y. Xing, B. Wang, and J. Wang, First-principles investigation of dynamical properties of molecular devices under a steplike pulse, Phys. Rev. B, 2010, 82(20): 205112
https://doi.org/10.1103/PhysRevB.82.205112
50 L. Zhang, Y. Xing, and J. Wang, First-principles investigation of transient dynamics of molecular devices, Phys. Rev. B, 2012, 86(15): 155438
https://doi.org/10.1103/PhysRevB.86.155438
51 P. My?h?nen, A. Stan, G. Stefanucci, and R. van Leeuwen, Kadanoff–Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime, Phys. Rev. B, 2009, 80(11): 115107
https://doi.org/10.1103/PhysRevB.80.115107
52 R. Gebauer, K. Burke, and R. Car, in: Time-Dependent Density Functional Theory, Lecture Notes in Physics, Vol. 706, edited by M. Marques, C. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E. U. Gross, Berlin Heidelberg: Springer, 2006: 463-477
https://doi.org/10.1007/3-540-35426-3_31
53 J. Jin, X. Zheng, and Y. Yan, Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach, J. Chem. Phys., 2008, 128(23): 234703
https://doi.org/10.1063/1.2938087
54 H. Tian and G. H. Chen, An efficient solution of Liouvillevon Neumann equation that is applicable to zero and finite temperatures, J. Chem. Phys., 2012, 137(20): 204114
https://doi.org/10.1063/1.4767460
55 H. Xie, F. Jiang, H. Tian, X. Zheng, Y. Kwok, S. Chen, C. Yam, Y. Yan, and G. H. Chen, Time-dependent quantum transport: an efficient method based on Liouville–von-Neumann equation for single-electron density matrix, J. Chem. Phys., 2012, 137(4): 044113
https://doi.org/10.1063/1.4737864
56 J. Hu, R. X. Xu, and Y. Yan, Communication: Padé spectrum decomposition of Fermi function and Bose function, J. Chem. Phys., 2010, 133(10): 101106
https://doi.org/10.1063/1.3484491
57 J. R. Soderstrom, D. H. Chow, and T. C. McGill, New negative differential resistance device based on resonant interband tunneling, Appl. Phys. Lett., 1989, 55(11): 1094
https://doi.org/10.1063/1.101715
58 M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F, 1985, 15(4): 851
https://doi.org/10.1088/0305-4608/15/4/009
59 F. Wang, C. Y. Yam, G. H. Chen, and K. Fan, Density matrix based time-dependent density functional theory and the solution of its linear response in real time domain, J. Chem. Phys., 2007, 126(13): 134104
https://doi.org/10.1063/1.2715549
60 G. Stefanucci, S. Kurth, E. Gross, and A. Rubio, in: Molecular and Nano Electronics: Analysis, Design and Simulation, Theoretical and Computational Chemistry, Vol. 17, edited by J. Seminario, Els<?Pub Caret?>evier, 2007: 247-284
61 C. Yam, X. Zheng, G. Chen, Y. Wang, T. Frauenheim, and T. A. Niehaus, Time-dependent versus static quantum transport simulations beyond linear response, Phys. Rev. B, 2011, 83(24): 245448
https://doi.org/10.1103/PhysRevB.83.245448
62 N. Sai, M. Zwolak, G. Vignale, and M. Di Ventra, Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems, Phys. Rev. Lett., 2005, 94(18): 186810
https://doi.org/10.1103/PhysRevLett.94.186810
63 F. Evers, F. Weigend, and M. Koentopp, Conductance of molecular wires and transport calculations based on densityfunctional theory, Phys. Rev. B, 2004, 69(23): 235411
https://doi.org/10.1103/PhysRevB.69.235411
64 G. Stefanucci and S. Kurth, Towards a description of the Kondo effect using time-dependent density-functional theory, Phys. Rev. Lett., 2011, 107(21): 216401
https://doi.org/10.1103/PhysRevLett.107.216401
65 E. Khosravi, A. M. Uimonen, A. Stan, G. Stefanucci, S. Kurth, R. van Leeuwen, and E. K. U. Gross, Correlation effects in bistability at the nanoscale: Steady state and beyond, Phys. Rev. B, 2012, 85(7): 075103
https://doi.org/10.1103/PhysRevB.85.075103
66 S. Kurth, G. Stefanucci, E. Khosravi, C. Verdozzi, and E. K. U. Gross, Dynamical Coulomb blockade and the derivative discontinuity of time-dependent density functional theory, Phys. Rev. Lett., 2010, 104(23): 236801
https://doi.org/10.1103/PhysRevLett.104.236801
67 P. My?h?nen, A. Stan, G. Stefanucci, and R. van Leeuwen, A many-body approach to quantum transport dynamics: Initial correlations and memory effects, Europhys. Lett., 2008, 84(6): 67001
https://doi.org/10.1209/0295-5075/84/67001
68 Y. Zhang, C. Y. Yam, and G. H. Chen, Dissipative timedependent quantum transport theory, J. Chem. Phys., 2013, 138(16): 164121
https://doi.org/10.1063/1.4802592
[1] Qiang Wang, Jian-Wei Li, Bin Wang, Yi-Hang Nie. First-principles investigation of quantum transport in GeP3 nanoribbon-based tunneling junctions[J]. Front. Phys. , 2018, 13(3): 138501-.
[2] Shmuel Gurvitz. Wave-function approach to Master equations for quantum transport and measurement[J]. Front. Phys. , 2017, 12(4): 120303-.
[3] Pei-Yun Yang,Wei-Min Zhang. Master equation approach to transient quantum transport in nanostructures[J]. Front. Phys. , 2017, 12(4): 127204-.
[4] Dazhi Xu,Jianshu Cao. Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach[J]. Front. Phys. , 2016, 11(4): 110308-110308.
[5] Xin-Qi Li. Number-resolved master equation approach to quantum measurement and quantum transport[J]. Front. Phys. , 2016, 11(4): 110307-.
[6] YiJing Yan,Jinshuang Jin,Rui-Xue Xu,Xiao Zheng. Dissipation equation of motion approach to open quantum systems[J]. Front. Phys. , 2016, 11(4): 110306-.
[7] Xiao-Fei Li, Yi Luo. Conductivity of carbon-based molecular junctions from ab-initio methods[J]. Front. Phys. , 2014, 9(6): 748-759.
[8] Jian-Sheng Wang, Bijay Kumar Agarwalla, Huanan Li, Juzar Thingna. Nonequilibrium Green’s function method for quantum thermal transport[J]. Front. Phys. , 2014, 9(6): 673-697.
[9] Ning Zhan-Yu(宁展宇), Qiao Jing-Si(乔婧思), Ji Wei(季威), Guo Hong(郭鸿). Correlation of interfacial bonding mechanism and equilibrium conductance of molecular junctions[J]. Front. Phys. , 2014, 9(6): 780-788.
[10] Wan-Ju Li, Dao-Xin Yao, E. W. Carlson. Tunable nano Peltier cooling device from geometric effects using a single graphene nanoribbon[J]. Front. Phys. , 2014, 9(4): 472-476.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed