Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Ryndyk, Dmitry A.; Gutiérrez, Rafael; Song, Boqun

doi:10.1007/978-3-642-02306-4_9

Cited by 66 publications

(81 citation statements)

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%

Comparison of electron and phonon transport in disordered semiconductor carbon nanotubes

et al. 2013

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Charge and thermal conductivities are the most important parameters of carbon nanomaterials as candidates for future electronics. In this paper we address the effects of Anderson type disorder in long semiconductor carbon nanotubes (CNTs) to electron charge conductivity and lattice thermal conductivity using the atomistic Green function approach. The electron and phonon transmissions are analyzed as a function of the length of the disordered nanostructures. The thermal conductance as a function of temperature is calculated for different lengths. Analysis of the transmission probabilities as a function of length of the disordered device shows that both electrons and phonons with different energies display different transport regimes, i.e. quasi-ballistic, diffusive and localization regimes coexist. In the light of the results we discuss heating of the semiconductor device in electronic applications.

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Section: Electron Transportmentioning

confidence: 99%

Comparison of electron and phonon transport in disordered semiconductor carbon nanotubes

et al. 2013

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“…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%

“…We here have taken the extended time (i.e. the contour variable) defined on the Schwinger-Keldysh closed time path, [21,17,19,18,20] Here it would be useful to mention that under the thermal equilibrium condition where temperature difference does not exist between ferromagnet and nonmagnetic metal, the O(J 2 Γ 0 ) term including no quantum fluctuations cannot contribute to spin pumping because of the balance between thermal fluctuations in ferromagnet and those in non-magnetic metal. [22] The second term of eq.…”

Section: Definitionmentioning

confidence: 99%

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Quantum Spin Pumping Mediated by Magnon

Nakata

2012

J. Phys. Soc. Jpn.

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We theoretically propose quantum spin pumping mediated by magnons, under a time-dependent transverse magnetic field, at the interface between a ferromagnetic insulator and a non-magnetic metal. The generation of a spin current under a thermal equilibrium condition is discussed by calculating the spin relaxation torque, which breaks the spin conservation law for conduction electrons and operates the coherent magnon state. Localized spins lose spin angular momentum by emitting magnons and conduction electrons flip from down to up by absorbing the momentum. The spin relaxation torque has a resonance structure as a function of the angular frequency of the applied transverse field. This fact is useful to enhance the spin pumping effect induced by quantum fluctuations. We also discuss the distinction between our quantum spin pumping theory and the one proposed by Tserkovnyak et al.

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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%

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Wacker

Pedersen

Karlström

et al. 2017

Computer Physics Communications

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QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), firstorder Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches. Keywords: Open quantum systems, Quantum dots, Anderson-type model, Coulomb blockade, Python Program summaryProgram Title: QmeQ Licensing provisions: BSD 2-Clause Programming language: Python External libraries: NumPy, SciPy, Cython Nature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads. Solution method: Exact diagonalisation of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach. Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

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Green Function Techniques in the Treatment of Quantum Transport at the Molecular Scale

Cited by 66 publications

References 303 publications

Comparison of electron and phonon transport in disordered semiconductor carbon nanotubes

Comparison of electron and phonon transport in disordered semiconductor carbon nanotubes

Quantum Spin Pumping Mediated by Magnon

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

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