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 pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.

Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics"

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• Models of Electrodes and Contacts in Molecular Electronics
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• Vibrational Instability due to Coherent Tunneling of Electrons
• Coherent probing of excited quantum dot states in an interferometer
• Coherent tunnelling through two quantum dots with Coulomb interaction
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• Fingerprints of mesoscopic leads in the conductance of a molecular wire
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Cited by in corpus (23)

• Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
• Spin Currents and Magnon Dynamics in Insulating Magnets
• Hybrid quantum magnetism in circuit-QED: from spin-photon waves to many-body spectroscopy
• Exceptional odd-frequency pairing in non-Hermitian superconducting systems
• Tunneling conductance and local density of states in tight-binding junctions
• Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling
• QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices
• Non-Hermitian Topology in Hermitian Topological Matter
• Transport signatures in topological systems coupled to AC fields
• First-principles quantum transport simulation of CuPc on Au(111) and Ag(111)
• Engineering interband tunneling in nanowires with diamond cubic or zincblende crystalline structure based on atomistic modeling
• Time-dependent electron transport through a strongly correlated quantum dot: multiple-probe open boundary conditions approach
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• First-principles molecular transport calculation for the benzenedithiolate molecule
• Quantum spin pumping mediated by magnon
• Conductance of graphene flakes contacted at their corners
• Quantifying the impact of phonon scattering on electrical and thermal transport in quantum dots
• PT-symmetric interference transistor
• Multiple perfectly-transmitting states of a single-level at strong coupling
• The temperature dependence of quantum spin pumping generated using electron spin resonance with three-magnon splittings
• Twin lead ballistic conductor based on nanoribbon edge transport
• A short note on spin pumping theory with Landau-Lifshitz-Gilbert equation under quantum fluctuation; necessity for quantization of localized spin
• Temperature dependence of spin currents in one- and three-dimensional insulators