2009
DOI: 10.1007/978-3-642-02306-4_9
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Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Abstract: The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pil… Show more

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Cited by 66 publications
(81 citation statements)
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References 303 publications
(375 reference statements)
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“…We refer the reader to Refs. [32][33][34][35] for details of the Green function technique. We neglect the electron-phonon coupling in this work since it is shown that electron-phonon mean free path in nanoscale carbon tubes and ribbons is tens of μm even at room temperature [36].…”
Section: Electron Transportmentioning
confidence: 99%
“…We refer the reader to Refs. [32][33][34][35] for details of the Green function technique. We neglect the electron-phonon coupling in this work since it is shown that electron-phonon mean free path in nanoscale carbon tubes and ribbons is tens of μm even at room temperature [36].…”
Section: Electron Transportmentioning
confidence: 99%
“…First, we briefly show the Langreth method, [12,18,19,20] which is useful to evaluate the perturbation expansion of the Keldysh ( or contour-ordered) Green's function [16,17,20,19,18] in subsection A.1. Second, we introduce the point of the bosonic Keldysh Green's functions [16,17,20,21] in subsection A.2.…”
Section: A Langreth Methodsmentioning
confidence: 99%
“…Second, we introduce the point of the bosonic Keldysh Green's functions [16,17,20,21] in subsection A.2. Last, the detailed calculations of eqs.…”
Section: A Langreth Methodsmentioning
confidence: 99%
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“…Modeling transport through such nanoscale systems is a complicated task, especially when strong Coulomb interaction is present in the quantum dots, as it can lead to phenomena like Coulomb blockade [7,8], Kondo effect [9,10,11], or Pauli blockade [12], just to mention a few. Quantum transport can be calculated using different theoretical methods like scatteringstates numerical-renormalization group [13], non-equilibrium Green's functions [14,15], and master equation based approaches [6,16,17,18,19,20,21,22].…”
Section: Introductionmentioning
confidence: 99%