Non-equilibrium Green's functions in density functional tight binding: method and applications

Pecchia, Alessandro; Penazzi, Gabriele; Salvucci, L; Carlo, Aldo Di

doi:10.1088/1367-2630/10/6/065022

Cited by 125 publications

(103 citation statements)

References 25 publications

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“…The scattering matrix can be found by a numerical diagonalization of the matrix E −Ĥ dot + iπŴŴ † . A more sophisticated treatment is to use a density functional theory, which treats interaction effects through a local density approximation (LDA), within this approximation one can solve from first principles the problem of the transmission through a molecular structure [146][147][148][149][150]. This was used to find the thermoelectric response and figure of merit of various molecules between metallic contacts, and thereby show how to engineer the transmission function; for example by adding side groups to the molecule which introduce Fano resonances at the right energy to generate a strong thermoelectric response [148,149].…”

Section: Transmission Functions For More Complicated Systemsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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In recent years, the study of heat to work conversion has been re-invigorated by nanotechnology. Steady-state devices do this conversion without any macroscopic moving parts, through steady-state flows of microscopic particles such as electrons, photons, phonons, etc. This review aims to introduce some of the theories used to describe these steady-state flows in a variety of mesoscopic or nanoscale systems. These theories are introduced in the context of idealized machines which convert heat into electrical power (heat-engines) or convert electrical power into a heat flow (refrigerators). In this sense, the machines could be categorized as thermoelectrics, although this should be understood to include photovoltaics when the heat source is the sun. As quantum mechanics is important for most such machines, they fall into the field of quantum thermodynamics. In many cases, the machines we consider have few degrees of freedom, however the reservoirs of heat and work that they interact with are assumed to be macroscopic. This review discusses different theories which can take into account different aspects of mesoscopic and nanoscale physics, such as coherent quantum transport, magnetic-field induced effects (including topological ones such as the quantum Hall effect), and single electron charging effects. It discusses the efficiency of thermoelectric conversion, and the thermoelectric figure of merit. More specifically, the theories presented are (i) linear response theory with or without magnetic fields, (ii) Landauer scattering theory in the linear response regime and far from equilibrium, (iii) Green-Kubo formula for strongly interacting systems within the linear response regime, (iv) rate equation analysis for small quantum machines with or without interaction effects, (v) stochastic thermodynamic for fluctuating small systems. In all cases, we place particular emphasis on the fundamental questions about the bounds on ideal machines. Can magnetic-fields change the bounds on power or efficiency? What is the relationship between quantum theories of transport and the laws of thermodynamics? Does quantum mechanics place fundamental bounds on heat to work conversion which are absent in the thermodynamics of classical systems?

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Section: Transmission Functions For More Complicated Systemsmentioning

confidence: 99%

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

et al. 2017

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“…The most popular is the approach combining density-functional theory (DFT) and NGF and known as DFT+NGF [246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268]. This method, however is not free from internal problems.…”

Section: Atomistic Transport Theorymentioning

confidence: 99%

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

Ryndyk

Gutiérrez²,

Song

2009

Springer Series in Chemical Physics

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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. In this chapter 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.

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“…Also in the ballistic case the above deformation of the integration contour can be taken advantage of [46].…”

Section: Discussionmentioning

confidence: 99%

“…Figure 2 shows schematically the different models relevant for LED simulations, and their couplings. Notice in particular that the Green's function library used in this work, libNEGF [25], accepts Hamiltonians from both atomistic and continuous media descriptions (shown as dashed arrows towards the NEGF box in the figure), like the empirical tight binding (ETB) or the envelope function approximation (EFA), respectively. Linear Elasticity is used to calculate the macroscopic description of mechanical strain, very important in III-nitrides in view of the large lattice mismatch between the constituents (In,Al,Ga)N. The local strain tensor is needed by the drift-diffusion and EFA modules, while the electrostatic potential ϕ is handed over to EFA or ETB for the calculation of the device Hamiltonian.…”

Section: Multiscale Coupling Schemesmentioning

confidence: 99%

“…In the continuous case, we use a piecewise linear finite element basis, which leads to a non-diagonal overlap matrix S. By subdividing the device into principal layers, each interacting only with its neighboring layer, the Hamiltonian and overlap matrix become organized in blocks (block-tridiagonal in 1D), and G r can be obtained by an iterative algorithm which scales linearly with the device length [46]. It has to be noted that this approach is effective only for calculations without or with only local interactions, whereas in more general cases the full Green's functions including non-local interactions may be needed.…”

Section: Schrödinger/drift-diffusion Calculationsmentioning

confidence: 99%

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Multiscale approaches for the simulation of InGaN/GaN LEDs

Maur

2015

J Comput Electron

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In this work we review basic aspects of multi-\ud scale approaches for combining atomistic with continuous\ud media descriptions and quantum mechanical with semiclassi-\ud cal driftdiffusion transport models for LED simulations. We\ud show how hybrid coupling of the Green's function formalism\ud with driftdiffusion simulations can give additional insight\ud into device behaviour without compromising too much com-\ud putational efficiency, and that the inclusion of atomistic tight-\ud binding calculations in a multiscale framework can help in\ud understanding specific features related to alloy fluctuations

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Non-equilibrium Green's functions in density functional tight binding: method and applications

Cited by 125 publications

References 25 publications

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

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

Multiscale approaches for the simulation of InGaN/GaN LEDs

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