Nonequilibrium Green’s functions

While quantum chemistry cannot be used to work with the Landauer/Buttiker/Imry formula as it stands, a very different approach based on nonequilibrium Green s functions yields a different formula (sometimes called the Caroli formula [68], or the NEGF formula in the Landauer/Imry/Buttiker limit). It is, for the current I ... 

Paulsson M, Brandbyge M (2007) Transmission eigenchannels from nonequilibrium Green s functions. Phys Rev B 76(11) 115117... 

Yeganeh S, Ratner MA, Mujica V (2007) Dynamics of charge transfer rate processes formulated with nonequilibrium Green s function. J Chem Phys 126 161103... 

Jauho AP (2003) Nonequilibrium Green function modeling of transport in mesoscopic systems. In Bonitz M, Semkat D (eds) Progress in nonequilibrium Green s functions II. World Scientific, Singapore... 

Quantum Correlation Effects in Electron Dynamics in Molecular Wires and Solar Cells The Nonequilibrium Green s Function Approach... 

In this work, we present a brief introduction to the nonequilibrium Green s function method and discuss two important examples in which nonequli-brium Green s functions can be employed (1) electric current calculations in molecular tunneling devices and (2) in quantum dot-sensitized solar cells. 

Before defining nonequilibrium Green s functions, we introduce field operators (e.g., a fermion field) y/ lr) and anticommutator relation t/r(r), t/rt(r )J = 5(r — r ). The Green s function on a Keldysh contour is defined as... 

Some interesting properties of nonequilibrium Green s functions can be proved. If we choose z = 0 (here corresponds to time on the upper... 

To understand the diagrammatic approach, which is introduced below, we first determine the nonequilibrium Green s functions for uncorrelated electrons in the leads and the bridge on a Keldysh contour employing a diagrammatic expansion rather than the equation of motion [45,52,53]. For such a system, the Hamiltonian is given by ... 

In this subsection, we calculate the Keldysh functions for the electrons in the bridge. Nonequilibrium Green s functions between the bridge, and left lead, and left-lead-bridge electrons are defined in the following way ... 

Nonequilibrium Green s functions for interacting bridge electrons... 

The applications of nonequilibrium Green s functions to the calculations of different molecular devices show the importance of electron correlation effects. The electron propagator method is able to explain experimental data and predict new electronic devices. 

For simplicity, the QD and SM indices in the e-ph constants have been omitted in Eq. (118) however, the frequencies and e-ph constants are obviously different in the both subsystems. In the proposed description, we assume that equilibrium Green s functions of the semiconductor and the quantum dot are known. However, to find QD equilibrium Green s function in a time-dependent field is not an easy task because it is not even clear whether Dyson equations for SM and QD Keldysh functions exist for different types of fermions interacting with each other. This problem is rather complicated even for molecular wires [54], Thus, we expect this problem to be even more complicated for solar cell systems where the interaction with light makes the problem essentially time dependent. In this section, we prove that Dyson equations for nonequilibrium Green s functions do exist. In our description, we adopt a graduate approach to the problem introducing different approximations step by step. As the first and the easiest step, we consider only uncorrelated electrons. 

M. Bonitz, R. Nareyka, D. Semkat, (Eds.), Progress in Nonequilibrium Green s Functions, World Scientific, Singapore, 2000. 

Nakamura, H. and Yamashita, K. (2005) Electron tunneling of photochemical reactions on metal surfaces nonequilibrium Green s function-density functional theory approach to photon energy dependence of reaction probability. J. Chem. Phys., 122, 194706-1-195706-13. 

Wang B, Yu Y, Zhang L, Wei Y, Wang J (2009) Oscillation of dynamic conductance of A1-C -A1 structures nonequilibrium Green s function and density functional theory study. Phys Rev B 79(15) 155117... 

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