Abstract
We start our theoretical analysis of MMM junctions transport properties by briefly introducing the concept of Green’s functions which are necessary for the development of the transport theory. A very thorough treatment of the Green’s functions properties and their quantum mechanical applications is given in numerous works on the subject. Here, we minimize mathematical intricacies by considering a system whose Hamiltonian H is independent of time.
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References
A. Aviram, M.A. Ratner, Molecular rectifiers. Chem. Phys. Lett. 29, 277–283 (1974)
S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005)
A.W. Ghosh, Electronics with molecules, in Comprehensive Semiconductor Science and Technology, vol. 5, ed. by P. Brattacharya, R. Fornari, H. Kamimura (Elsevier, Amsterdam, 2011), pp. 383–478
A. Mitra, I. Aleiner, A.J. Millis, Phonon effects in molecular transistors: quantal and classical treatment. Phys. Rev. B 69, 245302 (2004)
T. Mii, S.G. Tikhodeev, H. Ueba, Spectral features of inelastic electron transport via a localized state. Phys. Rev. B 68, 205406 (2003)
M. Galperin, M.A. Ratner, A. Nitzan, Inelastic electron tunneling spectroscopy in molecular junctions: peaks and dips. J. Chem. Phys. 121, 11965–11979 (2004)
M. Galperin, M.A. Ratner, A. Nitzan, Molecular transport junctions: vibrational effects. J. Phys.: Condens. Matter 19, 103201 (2007)
M. Galperin, A. Nitzan, M.A. Ratner, Inelastic effects in molecular junctions in the Coulomb and Kondo regimes: nonequilibrium equation-of-motion approach. Phys. Rev. B 76, 035301 (2007)
N.A. Zimbovskaya, Electron transport through a quantum dot in the Coulomb blockade regime: nonequilibrium Green’s function based model. Phys. Rev. B 78, 035331 (2008)
V. Mujica, M. Kemp, M.A. Ratner, Electron conduction in molecular wires. I. A scattering formalism. J. Chem. Phys. 101, 6849–6855 (1994)
N.A. Zimbovskaya, Low temperature electronic transport and electron transfer through organic macromolecules. J. Chem. Phys. 118, 4–7 (2003)
N.A. Zimbovskaya, Low-temperature electronic transport through macromolecules and characteristics of intramolecular electron transfer. J. Chem. Phys. 123, 114708 (2005)
J.L. D’Amato, G.M. Pastawski, Conductance of a disordered linear chain including inelastic scattering events. Phys. Rev. B 41, 7411–7420 (1990)
X.-Q. Li, Y.J. Yan, Scattering matrix approach to electronic dephasing in long-range electron transfer. J. Chem. Phys. 115, 4169–4174 (2001)
N.A. Zimbovskaya, G. Gumbs, Long-range electron transfer and electronic transport through macromolecules. Appl. Phys. Lett. 81, 1518–1520 (2002)
M. Buttiker, Role of quantum coherence in series resistors. Phys. Rev. B 33, 3020–3026 (1986)
C.W.J. Beenakker, Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44, 1646–1656 (1991)
D.V. Averin, A.N. Korotkov, K.K. Likharev, Theory of single-electron charging of quantum wells and dots. Phys. Rev. B 44, 6199–6211 (1991)
N. Simonian, J.J. Li, K.K. Likharev, Negative differential resistance at sequential single-electron tunnelling through atoms and molecules. Nanotechnology 18, 424006 (2007)
S. Datta, W. Tian, S. Hong, R. Reifenberger, J.I. Henderson, C.P. Kubiak, Current–voltage characteristics of self-assembled monolayers by scanning tunneling microscopy. Phys. Rev. Lett. 79, 2530–2533 (1997)
B. Muralidharan, A.W. Ghosh, S. Datta, Probing electronic excitations in molecular conduction. Phys. Rev. B 73, 155410 (2006)
S. Braig, P.W. Brouwer, Rate equations for Coulomb blockade with ferromagnetic leads. Phys. Rev. B 71, 195324 (2005)
Y. Meir, N.S. Wingreen, P.A. Lee, Transport through a strongly interacting electron system: theory of periodic conductance oscillations. Phys. Rev. Lett. 66, 3048–3051 (1991)
Y. Meir, N.S. Wingreen, P.A. Lee, Low-temperature transport through a quantum dot: the Anderson model out of equilibrium. Phys. Rev. Lett. 70, 2601–2604 (1993)
R. Swirkowicz, J. Barnas, M. Wilczynski, Electron tunnelling in a double ferromagnetic junction with a magnetic dot as a spacer. J. Phys.: Condens. Matter 14, 2011–2023 (2002)
R. Swirkowicz, J. Barnas, M. Wilczynski, Nonequilibrium Kondo effect in quantum dots. Phys. Rev. B 68, 195318 (2003)
V. Kashcheyev, A. Aharony, O. Entin-Wohlman, Applicability of the equations-of-motion technique for quantum dots. Phys. Rev. B 73, 125338 (2006)
A. Goker, Kondo resonance in an AC driven quantum dot subjected to finite bias. Solid State Commun. 148, 230–233 (2008)
G.D. Mahan, Many-Particle Physics (Plenum, New York, 2000)
A.B. Kaiser, Electronic transport properties of conducting polymers and carbon nanotubes. Rep. Prog. Phys. 64, 1–49 (2001)
A.N. Aleshin, H.J. Lee, Y.W. Park, K. Akagi, Coulomb-blockade transport in quasi-one dimensional polymer nanofibers. Phys. Rev. Lett. 93, 196601 (2004)
L. Siddiqui, A.W. Ghosh, S. Datta, Phonon runaway in carbon nanotube quantum dots. Phys. Rev. B 76, 085433 (2007)
N.A. Zimbovskaya, M.M. Kuklja, Vibration-induced inelastic effects in the electron transport through multisite molecular bridges. J. Chem. Phys. 131, 114703 (2009)
F. Elste, C. Timm, Transport through anisotropic magnetic molecules with partially ferromagnetic leads: spin-charge conversion and negative differential conductance. Phys. Rev. B 73, 235305 (2006)
L.P. Kadanoff, G. Baum, Quantum Statistical Mechanics. Green’s Function Method in Equilibrium and Nonequilibrium Problems (Benjamin, Reading, 1962)
M. Vagner, Expansions of nonequilibrium Green’s functions. Phys. Rev. B 44, 6104–6117 (1991)
E.N. Economou, Green’s Functions in Quantum Physics (Springer, New York, 2005)
N.S. Wingreen, K.W. Jacobsen, J.W. Wilkins, Resonant tunneling with electron-phonon interaction: an exactly solvable model. Phys. Rev. Lett. 61, 1396–1399 (1988)
N.S. Wingreen, K.W. Jacobsen, J.W. Wilkins, Inelastic scattering in resonant tunneling. Phys. Rev. B 40, 11834–11850 (1989)
A. Troisi, M.A. Ratner, Modeling the inelastic electron tunneling spectra of molecular wire junctions. Phys. Rev. B 72, 033408 (2005)
A. Troisi, M.A. Ratner, A. Nitzan, Vibronic effects in off-resonance molecular wire conductance. J. Chem. Phys. 118, 6072–6082 (2003)
L. Yan, Inelastic electron tunneling spectroscopy and vibrational coupling. J. Phys. Chem. A 110, 13249–13252 (2006)
S. Datta, Electric Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)
Y. Magarshak, J. Malinsky, A.D. Joran, Diagram techniques for solving Schwinger-Dyson equations: electron transfer pathways in biological molecules. J. Chem. Phys. 95, 418–431 (1991)
J. Bonca, S.A. Trugman, Inelastic quantum transport. Phys. Rev. Lett. 79, 4874–4877 (1997)
H. Ness, Quantum inelastic electron-vibration scattering in molecular wires: Landauer-like versus Green’s function approaches and temperature effects. J. Phys.: Condens. Matter 18, 6307–6328 (2006)
Y. Zhou, M. Freitag, J. Hone, C. Staii, A.T. Johnson, N.J. Pinto, A.G. MacDiarmid, Fabrication and electrical characterization of polyaniline-based nanofibers with diameter below 30 nm. Appl. Phys. Lett. 83, 3800–3802 (2003)
A.G. MacDiarmid, Nobel lecture: synthetic metals: a novel role for organic polymers. Rev. Mod. Phys. 73, 701–712 (2001)
J. Joo, Z. Oblakowski, G. Du, J.P. Pouget, E.J. Oh, J.M. Wiesinger, Y. Min, A.G. MacDiarmid, A.J. Epstein, Microwave dielectric response of mesoscopic metallic regions and the intrinsic metallic state of polyaniline. Phys. Rev. B 49, 2977–2980 (1994)
J.P. Pouget, Z. Oblakowski, Y. Nogami, P.A. Albouy, M. Laridjani, E.J. Oh, Y. Min, A.G. MacDiarmid, J. Tsukamoto, T. Ishiguro, A.J. Epstein, Recent structural investigations of metallic polymers. Synth. Met. 65, 131–140 (1994)
M. Pollak, C.J. Adkins, Conduction in granular metals. Philos. Mag. B 65, 855–860 (1992)
V.N. Prigodin, A.J. Epstein, Nature of insulator-metal transition and novel mechanism of charge transport in the metallic state of highly doped electronic polymers. Synth. Met. 125, 43–53 (2001)
C.J. Bolton-Heaton, C.J. Lambert, V.I. Falko, V.N. Prigodin, A.J. Epstein, Distribution of time constants for tunneling through a one-dimensional disordered chain. Phys. Rev. B 60, 10569–10572 (1999)
N.A. Zimbovskaya, A.T. Johnson, N.J. Pinto, Electronic transport mechanism in conducting polymer nanofibers. Phys. Rev. B 72, 024213 (2005)
N.A. Zimbovskaya, Inelastic electron transport in polymer nanofibers. J. Chem. Phys. 123, 114705 (2008)
H. Hang, A.-P. Jauho, Quantum Kinetics in Transport and Optics in Semiconductors (Springer, Berlin, 1996)
K.-C. Chou, Z.-B. Su, B.-L. Hao, L. Yu, Equilibrium and nonequilibrium formalisms made unified. Phys. Rep. 118, 1–131 (1984)
B.-L. Hao, Closed time path Green’s functions and nonlinear response theory. Physica A 109, 221–236 (1981)
E. Wang, U. Heinz, Generalized fluctuation-dissipation theorem for nonlinear response functions. Phys. Rev. D 66, 025008 (2002)
S. Mukamel, Principles of Nonlinear Optical Spectroscopy (University Press, New York, 1995)
U. Harbola, S. Mukamel, Non-equilibrium superoperator GW-equations. J. Chem. Phys. 124, 044106–044117 (2006)
U. Harbola, S. Mukamel, Superoperator nonequilibrium Green’s function theory of many-body systems; applications to charge transfer and transport in open junctions. Phys. Rep. 465, 191–222 (2008)
Y. Meir, N.S. Wingreen, Landauer formula for the current through an interacting electron region. Phys. Rev. Lett. 68, 2512–2515 (1992)
A.P. Jauho, N.S. Wingreen, Y. Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems. Phys. Rev. B 50, 5528–5544 (1994)
N.S. Wingreen, Y. Meir, Anderson model out of equilibrium: Noncrossing-approximation approach to transport through a quantum dot. Phys. Rev. B 49, 11040–11052 (1994)
J. Inarrea, G. Platero, A.H. MacDonald, Electronic transport through a double quantum dot in the spin-blockade regime: theoretical models. Phys. Rev. B 76, 085329 (2007)
L.Y. Gorelik, A. Isacsson, M.V. Voinova, B. Kasemo, R.I. Shekhter, M. Jonson, Shuttle mechanism for charge transfer in Coulomb blockade nanostructures. Phys. Rev. Lett. 80, 4526–4529 (1998)
N.M. Chtchelkatchev, W. Belzig, C. Bruder, Charge transport through a single-electron transistor with a mechanically oscillating island. Phys. Rev. B 70, 193305 (2004)
Ya.M. Blanter, O. Usmani, Yu.V. Nazarov, Single-electron tunneling with strong mechanical feedback. Phys. Rev. Lett. 93, 136802 (2004)
C.B. Doiron, W. Belzig, C. Bruder, Electrical transport through a single-electron transistor strongly coupled to an oscillator. Phys. Rev. B 74, 205336 (2006)
K.D. McCarthy, N. Prokofiev, M.T. Tuominen, Incoherent dynamics of vibrating single-molecule transistors. Phys. Rev. B 67, 245415 (2003)
J. Koch, M. Semmelhack, F. von Oppen, A. Nitzan, Current-induced nonequilibrium vibrations in single-molecule devices. Phys. Rev. B 73, 155306 (2006)
J. Koch, F. von Oppen, Franck-Condon blockade and giant Fano factors in transport through single molecules. Phys. Rev. Lett. 94, 206804 (2005)
J. Koch, F. von Oppen, Effects of charge-dependent vibrational frequencies and anharmonicities in transport through molecules. Phys. Rev. B 72, 113308 (2005)
J. Koch, M.E. Raikh, F. von Oppen, Pair tunneling through single molecules. Phys. Rev. Lett. 96, 056803 (2006)
H. Ueba, T. Mii, N. Lorente, B.N.J. Persson, Adsorbate motions induced by inelastic-tunneling current: theoretical scenarios of two-electron processes. J. Chem. Phys. 123, 084707 (2005)
S. Braig, K. Flensberg, Vibrational sidebands and dissipative tunneling in molecular transistors. Phys. Rev. B 68, 205324 (2003)
D.A. Ryndyk, P. D’Amico, K. Richter, Single-spin polaron memory effect in quantum dots and single molecules. Phys. Rev. B 81, 115333 (2010)
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Zimbovskaya, N.A. (2013). Transport Theory. In: Transport Properties of Molecular Junctions. Springer Tracts in Modern Physics, vol 254. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8011-2_2
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DOI: https://doi.org/10.1007/978-1-4614-8011-2_2
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