Non-equilibrium Green’s function theory for non-adiabatic effects in quantum transport: Inclusion of electron-electron interactions

Kershaw, Vincent F.; Kosov, Daniel S.

doi:10.1063/1.5058735

Cited by 11 publications

(18 citation statements)

References 93 publications

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“…Therefore the small parameter in our theory is Ω Γ . The solution described below follows closely the ideas of previous authors 36,[56][57][58][59]63 . The exponential operators in Eqs.…”

Section: B Non-adiabatic Expansion Of Kadanoff-baym Equations In Wigmentioning

confidence: 84%

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

2020

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Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of the Kadanoff-Baym equations in the Wigner space. As a result, analytical expressions for dynamical corrections to the adiabatically computed Green's functions are produced. These dynamical corrections depend not only on the instantaneous molecular geometry but also on the nuclear velocities. To make the theoretical approach fully self-consistent, the same time-separation approach is used to develop expressions for the adiabatic, dissipative, and stochastic components of current-induced forces in terms of adiabatic Green's functions. Using these current induced forces, the equation of motion for the nuclear degrees of freedom is cast in the form of a Langevin equation. The theory is applied to model molecular electronic junctions. We observe that the interplay between the value of the spring constant for the molecule-electrode chemical bond and electronic coupling strength to the corresponding electrode is critical for the appearance of structural instabilities and, consequently, telegraphic switching in the electric current. The range of model parameters is identified to observe structurally stable molecular junctions as well as various different kinds of current-induced telegraphic switching. The interfacial structural instabilities are also quantified based on current noise calculations.

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Section: B Non-adiabatic Expansion Of Kadanoff-baym Equations In Wigmentioning

confidence: 84%

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

2020

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“…(10). Equations ( 7) and ( 10) can be considered to be a Liouville space extension of the spectral Green's function formalism in Hilbert space [10][11][12]. There are noteworthy analogies to quantum field theory.…”

Section: Spectral Green's Functions For the Lindblad Master Equationmentioning

confidence: 99%

“…Indeed, the former requires only an operator inversion, while the latter needs either calculation of an operator exponent or an operator diagonalization. In addition, the knowledge of the poles and residues of the rational structure (12) and Eq. ( 8) can be used to evaluate the steady state once for all values of the spectral parameter, thus justifying the importance of the method for spectroscopy.…”

Section: Spectral Green's Functions For the Lindblad Master Equationmentioning

confidence: 99%

“…This method is based on the approximate calculation of correlations between dynamic operators that leads to selfconsistent equations for the observables. Subsequently, this method was extended to nonequilibrium closed and non-Markovian open quantum systems describing various transport phenomena where, besides the standard time-domain formalism, it was transformed to an inhomogeneous spectral problem in Hilbert space [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Spectral Green's-function method in driven open quantum dynamics

Karabanov

Köckenberger

2021

Phys. Rev. A

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A method based on spectral Green's functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space formalism and provides simple algebraic connections between the driven and nondriven dynamics in the spectral frequency domain. The formalism shows remarkable analogies to the use of Green's functions in quantum field theory, such as the elementary excitation energies and the Dyson self-energy equation.To demonstrate its potential, we apply the method to a coherently driven dissipative ensemble of two-level systems comprising a single "active" subsystem interacting with N "passive" subsystems-a generic model with important applications in quantum optics and dynamic nuclear polarization. The method dramatically reduces the computational cost compared with simulations based on solving the full master equation, thus making it possible to study and optimize many-body correlated states up to the physically realistic limit of an arbitrarily large N.

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“…This means that for all Green's functions G(t, t ′ ), the slow time-dependent external field implies that G(T + τ /2, T − τ /2) varies slowly with the central time T , but oscillates fast with the relative time τ . This idea has been often used to separate classical (slow) and quantum (fast) degrees of freedom using NEGF theory [46][47][48][49][50][51][52][53][54] .…”

Section: B Gradient Expansion Of Wigner Space Kadanoff-baym Equationsmentioning

confidence: 99%

Timescale separation solution of the Kadanoff-Baym equations for quantum transport in time-dependent fields

Honeychurch¹,

Kosov²

2019

Phys. Rev. B

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The interaction with time-dependent external fields, especially the interplay between timedependent driving and quantum correlations, changes the familiar picture of electron transport through nanoscale systems. Although the exact solution of the problem of AC quantum transport of noninteracting electrons has been known for more than two decades, the treatment of correlated particles presents a significant theoretical challenge. In this paper, using the perturbative separation of fast electron tunnelling and slow driving time-scales, we developed a practical approach for timedependent quantum transport with nonequilibrium Green's functions. The fast electronic dynamics is associated with relative time whilst the slow driving is related to the central time in the Green's functions. The ratio of characteristic electron tunneling time over the period of harmonic driving is used as a small parameter in the theory to obtain a convergent time-derivative expansions of the Green's functions. This enables the algebraic solution of the Kadanoff-Baym equations in Wigner space. Consequently, we produced analytical expressions for dynamical corrections to advanced, retarded, and lesser Green's functions, as well as an improved expression for AC electric current. The method developed is applicable to the general case of multi-channel electron transport through a correlated central region. The theory is applied to different transport scenarios: time-dependent transport through a driven single-resonant level is compared to exact results; and electron transport through a molecular junction described by the Holstein model with a time-oscillating voltage bias is also investigated.

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Non-equilibrium Green’s function theory for non-adiabatic effects in quantum transport: Inclusion of electron-electron interactions

Cited by 11 publications

References 93 publications

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

Spectral Green's-function method in driven open quantum dynamics

Timescale separation solution of the Kadanoff-Baym equations for quantum transport in time-dependent fields

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