We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-Hermitian Liouvillian in super-Fock space. We transform the Liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree–Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.

Super-fermion representation of quantum kinetic equations for the electron transport problem.

New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields non-perturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.

https://arxiv.org/pdf/cond-mat/0509442.pdf

The influence of ultra-fast laser pulses on electron transfer in molecular wires studied by a non-Markovian density matrix approach

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville–Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron–vibronic and electron–electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

Nonequilibrium perturbation theory in Liouville–Fock space for inelastic electron transport

The quantum transport via a donor (D)−bridge (B)−acceptor (A) single molecule is studied using density functional theory in conjunction with the Landauer−Buttiker formalism. Asymmetric electrical response for opposite biases is observed resulting in significant rectification in current. The intrinsic dipole moment induced by substituent side groups in the molecule leads to enhanced/reduced polarization of the system under a forward/reverse applied potential, thus asymmetry in the charge distribution and the electronic current under bias. Under a forward bias, the energy gap between the D and A frontier orbitals closes and the current increases rapidly, whereas under a reverse bias, the D−A gap widens and the current remains small.

/pdf/asymmetric-currents-in-a-donor-bridge-acceptor-single-2fu7t6wqvc.pdf

Asymmetric Currents in a Donor−Bridge−Acceptor Single Molecule: Revisit of the Aviram−Ratner Diode

Correlated, ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical formalism is developed for the calculation of retarded and advanced Green functions in terms of the electron propagator matrix for a bridge molecule. The calculation of the current requires integration in a complex half-plane for a trace that involves terminal and Green function matrices that may have any rank. Because the latter arrays have poles represented by matrices, an alternative expression is developed in terms of ordinary poles which are (n−1)-fold degenerate or nondegenerate. For an arbitrary number of terminal orbitals, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator, i.e., the parameters that are found in the output of numerical calculations.

Ab initio electron propagator theory of molecular wires. II. Multiorbital terminal description

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green’s-function matrices. Because the Green’s-function matrices have complex poles represented by matrices, a special scheme is developed to express these “matrix poles” in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.

Ab initio electron propagator theory of molecular wires. I. Formalism.

Correlated ab initio electron propagators provide a systematic approach to treating correlation effects in the study of molecular wires. Some preliminary formal and computational steps toward the application of such methods to electron transport problems in nanoscience are presented. Retarded and advanced Green functions are expressed in terms of a general electron propagator for a bridge molecule. Terminal and Green function matrices of any rank may be employed. An analytical expression for the current depends on correlated electron binding energies, pole strengths, and Dyson orbitals that may be produced with readily available software. Calculations on benzene dithiolate between gold atoms illustrate the capabilities of this approach. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Correlated Ab initio electron propagators in the study of molecular wires

In this work we study the effect of electron correlations in molecular transistors with molecular bridges based on 1,4-benzene-dithiol (BDT) and 2-nitro-1,4-benzene-dithiol (nitro-BDT) by using ab initio electron propagator calculations. We find that there is no gate field effect for the BDT based transistor in accordance with the experimental data. After verifying the computational method on the BDT molecule, we consider a transistor with a nitro-BDT molecular bridge. From the electron propagator calculations, we predict strong negative differential resistance at small positive and negative values of source-drain voltages. The explanation of the peak and the minimum in the current is given in terms of the molecular orbital picture and switch-on (-off) properties due to the voltage dependencies of the Dyson poles (ionization potentials). When the current is off, the electronic states on both electrodes are populated resulting in the vanishing tunneling probability due to the Pauli principle. Besides the m...

Molecular transistors based on BDT-type molecular bridges.

A correlated, ab initio electron propagator approach is tested for a model system containing 1,4-benzene-dithiolate attached to two gold or two aluminum atoms. Qualitative agreement with available experiment is achieved for the gold dithiolate system. Similar current and conductance curves obtain for both metal leads when the Fermi energy is set to −1.0 eV. A molecular orbital analysis is given for the gold dithiolate system. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Correlated, ab initio electron propagators in the study of molecular wires: Application to a single molecular bridge placed between two model leads

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