Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We use the Heisenberg picture to facilitate dynamic theory and propose a new systematic method of collecting the basis vectors spanning the Liouville space, which is the most crucial step in obtaining the resolvent Green's function. We obtain all the linearly independent basis vectors for studying the single-impurity Anderson models with one and two reservoirs. The latter is an appropriate model for studying the Kondo phenomenon in a steady state when a bias is applied. This is one of long standing subjects in theoretical condensed matter physics.
We develop a nonperturbative dynamical theory (NDT) that is useful for treating nonequilibrium transport in a system with strong correlation. We apply our NDT to the single-impurity Anderson model in equilibrium to check its reliability by comparing with the results of numerical renormalization group method (NRG). We finally suggest a self-consistent loop to calculate the current in a lead-dot-lead system with Kondo coupling.
We develop a nonperturbative dynamical theory (NDT) to calculate the retarded Green's function under nonequilibrium conditions. The NDT is particularly useful for treating nonequilibrium transport problems in systems with strong correlation. We apply our NDT to the well-known single-impurity Anderson model at equilibrium to determine its feasibility. We then apply it to a nonequilibrium transport problem in a system with Kondo coupling. An Anderson model with two metallic reservoirs is studied to understand the phenomenon of Kondo-peak splitting in a single-electron transistor of mesoscopic si…
In the previous paper, we found a series expression for the average electric current following a quench in the nonequilibrium Kondo model driven by a bias voltage. Here, we evaluate the steady state current in the regimes of strong and weak coupling. We obtain the standard leading order results in the usual weak antiferromagnetic regime, and we also find a new universal regime of strong ferromagnetic coupling with Kondo temperature $T_K = D e^{\frac{3π^2}{8} ρJ}$. In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temper…
The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic reservoir. Using …
A nonequilibrium Green's functions (NEGF) approach for spatially inhomogeneous, strongly correlated artificial atoms is presented and applied to compute the time-dependent properties while starting from a (correlated) initial few-electron state at finite temperatures. In the regime of moderate to strong coupling, we consider the Kohn mode of a three-electron system in a parabolic confinement excited by a short pulsed classical laser field treated in dipole approximation. In particular, we numerically confirm that this mode is preserved within a conserving (e.g. Hartree-Fock or second Born) the…
We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantitie…
The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a co…
We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.
The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contribut…
We study the time and space resolved dynamics of a qubit with an Ohmic coupling to propagating 1D photons, from weak coupling to the ultrastrong coupling regime. A nonperturbative study based on Matrix Product States (MPS) shows the following results: (i) The ground state of the combined systems contains excitations of both the qubit and the surrounding bosonic field. (ii) An initially excited qubit equilibrates through spontaneous emission to a state, which under certain conditions, is locally close to that ground state, both in the qubit and the field. (iii) The resonances of the combined qu…
We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular junctions. Within the technique intra-system interactions are taken into account exactly, while molecular coupling to contacts is used as a small parameter in perturbative expansion. We demonstrate the viability of the approach with numerical simulations for a generic junction model of quantum dot coupled to two electron reservoirs.
Stationary electric transport in semiconductor nanostructures is studied by the method of nonequilibrium Green functions. In the case of sequential tunneling the results are compared with density matrix theory, providing almost identical results. Nevertheless, the method of Green functions is easier to handle due to the availability of an absolute energy scale. It is demonstrated, that the transport in complicated structures, like quantum cascade lasers, can be described in reasonable agreement with experiment.
We present a formulation of a nonequilibrium Green's function method for thermal current in nanojunction atomic systems with nonlinear interactions. This first-principle approach is applied to the calculation of the thermal conductance in carbon nanotube junctions. It is shown that nonlinearity already becomes important at low temperatures. Nonlinear interactions greatly suppress phonon transmission at room temperature. The peak of thermal conductance is found to be around 400K, in good agreement with experiments. High-order phonon scattering processes are important for diffusive heat transpor…
We investigate the effects of alternating voltage on nonequilibrium quantum systems with localised phonon modes. Nonequilibrium Green's functions are utilised, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and foun…
In this paper, spin-dependent transport through a spin diode composed of a quantum dot coupled to a normal metal and a ferromagnetic lead is studied. The current polarization and the spin accumulation are analyzed using the equations of motion method within the nonequilibrium Green's function formalism. We present a suitable method for computing Green's function without carrying out any self-consistent calculation. The influence of coupling strength and magnetic field on the spin current is studied and observed that this device cannot work as a spin diode under certain conditions.
A generalized Landauer formula, derived with the methods due to Keldysh, and Baym and Kadanoff, is gaining widespread use in the modeling of transport in a large number of different mesoscopic systems. We review some of the recent developments, including transport in semiconductor superlattices, calculation of noise, and nanoelectromechanical systems.
An open quantum system consists of leads connected to a device of interest. Within the nonequilibrium Green's function technique, we examine the replacement of leads by self-energies in continuum calculations. Our starting point is a formulation of the problem for continuum systems by T.E. Feuchtwang. In this approach there is considerable flexibility in the choice of unperturbed Green's functions. We examine the consequences of this freedom on the treatment of leads. For any choice the leads can be replaced by coupling self-energies which are simple functions of energy. We find that the retar…
Here we address two nonequilibrium Green's functions approaches for a resonant tunneling structure under a sudden switch of a bias. Our aim is to stress that the time-dependent Keldysh formulation of Jauho, Wingreen and Meir, and the partition-free scheme of Stefanucci and Almbladh are formally equivalent in the ubiquitous case of wide-band limit and noninteracting electrons, if leads and dot are in equilibrium before the time-dependent perturbation. We develop explicit closed formulas of the lesser Green's function and time-dependent current, reminding that the different integration limits pr…
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and introduce superoperator algebra that greatly simplifies the derivation and the physical interpretation of all quantities. Expressions for various observables are derived directly in real time in terms of superoperator nonequilibrium Green's functions (SNGF), rather than the artificial time-loop required in Schwinger's Hilbert-space formulation. Applications for com…
We give nonequilibrium Green's function (NEGF) perspective on thermodynamics formulations for open quantum systems strongly coupled to baths. Scattering approach implying thermodynamic consideration of a super-system (system plus baths) weakly coupled to external super-baths is compared with consideration of thermodynamics of a system strongly coupled to its baths. We analyze both approaches from the NEGF perspective and argue that the latter yields a possibility of thermodynamic formulation consistent with dynamical (quantum transport) description.
We present a theory of molecular motors based on the Ehrenfest dynamics for the nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations for the current-induced forces. Electron-electron interactions can be systematically included through many-body perturbation theory, making the nonequilibrium Green's functions formulation suitable for first-principles treatments of realistic junctions. The method is benchmarked against simulations via real-time Kadanoff-Baym equations, finding an excellent agreement. Results on a paradigmatic model of molecular motor show that correlations …
We study the nonlinear elastic quantum electronic transport properties of nanoscopic devices using the Nonequilibrium Green's function (NEGF) method. The Green's function method allows us to expand the $I-V$ characteristics of a given device to arbitrary powers of the applied voltages. By doing so, we are able to relate the NEGF method to the scattering approach, showing their similarities and differences and calculate the conductance coefficients to arbitrary order. We demonstrate that the electronic current given by NEGF is gauge invariant to all orders in powers of $V$, and discuss the requ…
Time-dependent nonequilibrium Green's functions (TDNEGF) are shown to provide a flexible, effective tool for the description of quantum mechanical single particle scattering on a spatially localized, time-dependent potential. Focusing on numerical methods, arbitrary space and time dependence of the potential can be treated, provided it is zero before an initial time instant. In this case, appropriate version of the Dyson and Keldysh equations lead to a transparent description with clear physical interpretation. The interaction of a short laser pulse and an electron propagating initially in fre…
The role of multimode vibrational dynamics in electron transport through single molecule junctions is investigated. The study is based on a generic model, which describes charge transport through a single molecule that is attached to metal leads. To address vibrationally-coupled electron transport, we employ a nonequilibrium Green's function approach that extends a method recently proposed by Galperin et al. [Phys. Rev. B 73, 045314 (2006)] to multiple vibrational modes. The methodology is applied to two systems: a generic model with two vibrational degrees of freedom and benzenedibutanethiola…
This paper is devoted to the study and interpretation of the spectral function $\mathbf{A}(ω, T)$ of the Keldysh nonequilibrium Green's function. The spatial diagonal of the spectral function is often interpreted as a time-dependent local density of states. We show that this object can take negative values implying that a simple probability interpretation as a time-dependent density of states is not possible. The same issue also occurs for the Wigner function $P(x,p)$ where it is solved by taking the uncertainty principle into account. We follow the same path and incorporate the time-energy un…
Excitonic contributions to absorption and photocurrent generation in semiconductor nanostructures are described theoretically and simulated numerically using steady-state non-equilibrium Green's function theory. In a first approach, the coherent interband polarization including Coulomb corrections is determined from a Bethe-Salpeter-type equation for the equal time interband single-particle charge carrier Green's function. The effects of excitonic absorption on photocurrent generation are considered on the same level of approximation via the derivation of the corresponding corrections to the e…
We review a recent theoretical development based on non-equilibrium Green's function formalism to study heat transport in nanomechanical devices modeled by phononic systems of coupled quantum oscillators driven by ac forces and connected to phononic reservoirs. We present the relevant equations to calculate the heat currents flowing along different regions of the setup, as well as the power developed by the time-dependent forces. We also present different strategies to evaluate the Green's functions exactly or approximately within the weak driving regime. We finally discuss the different mecha…
Due to random dopant fluctuations, the device-to-device variability is a serious challenge to emerging nanoelectronics. In this work we present theoretical formalisms and numerical simulations of quantum transport variability, based on the nonequilibrium Green's functions and the multiple scattering theory. We have developed a general formalism using the diagrammatic technique within the coherent potential approximation (CPA) that can be applied to a wide range of disorder concentrations. In addition, we have developed a method by using a perturbative expansion within the low concentration app…
We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory in molecular coupling to radiation field we perform simulations employing realistic parameters. Results of the simulations are compared to the bare perturbation theory (PT) usually employed in studies on nonlinear optical …
We study the high- and low-voltage properties of the out-of-equilibrium Anderson model for quantum dots, using a functional method in the Keldysh formalism. The Green's function at the impurity site can be regarded as a functional of a nonequilibrium distribution function. The dependence of the Green's function on the bias voltage V and temperature T arises through the nonequilibrium distribution function. From this behavior as a functional, it is shown that the nonequilibrium Green's function at high-voltage limit is identical to the equilibrium Green's function at high-temperature limit. Thi…
We study the dynamics of the biased sub-Ohmic spin-boson model by means of a time-dependent variational matrix product state (TDVMPS) algorithm. The evolution of both the system and the environment is obtained in the weak- and the strong-coupling regimes, respectively characterized by damped spin oscillations and by a nonequilibrium process where the spin freezes near its initial state, which are explicitly shown to arise from a variety of reactive environmental quantum dynamics. We also explore the rich phenomenology of the intermediate-coupling case, a nonperturbative regime where the system…
We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident p…
Real-time Green's function simulations of molecular junctions (open quantum systems) are typically performed by solving the Kadanoff-Baym equations (KBE). The KBE, however, impose a serious limitation on the maximum propagation time due to the large memory storage needed. In this work we propose a simplified Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA) to overcome the KBE limitation on time, significantly speed up the calculations, and yet stay close to the KBE results. This is achieved through a twofold advance: first we show how to make the GKBA work in open…
A quantum transport model incorporating spin scattering processes is presented using the non-equilibrium Green's function (NEGF) formalism within the self-consistent Born approximation. This model offers a unified approach by capturing the spin-flip scattering and the quantum effects simultaneously. A numerical implementation of the model is illustrated for magnetic tunnel junction devices with embedded magnetic impurity layers. The results are compared with experimental data, revealing the underlying physics of the coherent and incoherent transport regimes. It is shown that small variations i…
With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green's function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach f…
In this work, we explore the possibility of emergent nonequilibrium steady states arising from the electric-field-driven Mott insulator via the Keldysh-Floquet dynamical mean field theory (DMFT), which can determine the fully-interacting, nonequilibrium steady-state Green's functions with the noninteracting counterparts as an input to the DMFT self-consistency loop. Unlike the retarded component, obtaining the lesser Green's function for the noninteracting system presents an important obstacle since the thermalization of the noninteracting system still requires a precise understanding of the d…
An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage. In the implementation, accurate and efficient methods are developed especially for evaluation of the density matrix and treatment of boundaries between the scattering region and the leads. Equilibrium and nonequilibrium contributions in the density matrix are evaluated with very high precision by a contour …
We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast timescales in the equations of motion for the Green's functions by means of the Wigner representation. Time derivatives with respect to central time serves as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce series of analytic expressions for …
The influence of electron--phonon interactions on the dynamics of a quantum dot coupled to a photonic cavity mode is investigated using a nonequilibrium Green's function approach. Within a polaron frame, the self-consistent-Born approximation is used to treat the phonon-assisted scattering processes between the quantum dot polaron and the cavity. Two-time correlators of the quantum dot-cavity system are calculated by solving the Kadanoff-Baym equations, giving access to photon spectra and photon indistinguishability. The non-Markovian nature of the interaction with the phonon bath is shown to …
Many-body transport has emerged as an efficient tool for understanding interaction effects in quantum materials with a multi-band electronic structure. This paper proposes a formula for the two-particle transmission coefficient for Cooper-pair transport between multi-band normal and superconducting materials. The approach employs a tight-binding nonequilibrium Green's function technique, allowing a direct calculation of the two-particle current, without invoking the paradigm of Andreev reflection. As an application of the theory, we demonstrate a low-field linear magnetoresistance effect for s…
The transport and gain properties of quantum cascade (QC) structures are investigated using a nonequilibrium Green's function (NGF) theory which includes quantum effects beyond a Boltzmann transport description. In the NGF theory, we include interface roughness, impurity, and electron-phonon scattering processes within a self-consistent Born approximation, and electron-electron scattering in a mean-field approximation. With this theory we obtain a description of the nonequilibrium stationary state of QC structures under an applied bias, and hence we determine transport properties, such as the …
This review deals with the nonequilibrium Green's function (NEGF) method applied to the problems of energy transport due to atomic vibrations (phonons), primarily for small junction systems. We present a pedagogical introduction to the subject, deriving some of the well-known results such as the Laudauer-like formula for heat current in ballistic systems. The main aim of the review is to build the machinery of the method so that it can be applied to other situations, which are not directly treated here. In addition to the above, we consider a number of applications of NEGF, not in routine mode…
In a recent publication [W. Dou, G. Miao, and J. E. Subotnik, Phys. Rev. Lett. 119, 046001 (2017)], using the quantum-classical Liouville equation (QCLE), we derived a very general form for the electronic friction felt by a molecule moving near one or many metal surfaces. Moreover, we have already proved the equivalence of the QCLE electronic friction with the Head-Gordon--Tully model as well as a generalized version of von Oppen's nonequilibrium Green's function (NEGF) method at equilibrium [W. Dou and J. E. Subotnik, Phys. Rev. B 96, 104305 (2017)]. In the present paper, we now further prove…
We formulate and apply a nonperturbative numerical approach to the nonequilibrium current, $I(V)$, through a voltage-biased molecular conductor. We focus on a single electronic level coupled to an unequilibrated vibration mode (Anderson-Holstein model), which can be mapped to an effective three-state problem. Performing an iterative summation of real-time path integral (ISPI) expressions, we accurately reproduce known analytical results in three different limits. We then study the crossover regime between those limits and show that the Franck-Condon blockade persists in the quantum-coherent lo…
Phonon-phonon interaction is systematically studied by nonequilibrium Green's function (NEGF) formulism in momentum space at finite temperatures. Within the quasi-particle approximation, phonon frequency shift and lifetime are obtained from the retarded self-energy. The lowest order NEGF provides the same phonon lifetime as Fermi's golden rule. Thermal conductance is predicted by the Landauer formula with a phenomenological transmission function. The main advantage of our method is that it covers both ballistic and diffusive limits and thermal conductance of different system sizes can be easil…
Using non-equilibrium Green functions we calculate the spin-polarized current and shot noise in a ferromagnet--quantum-dot--ferromagnet (FM-QD-FM) system. Both parallel (P) and antiparallel (AP) magnetic configurations are considered. Coulomb interaction and coherent spin-flip (similar to a transverse magnetic field) are taken into account within the dot. We find that the interplay between Coulomb interaction and spin accumulation in the dot can result in a bias-dependent current polarization $\wp$. In particular, $\wp$ can be suppressed in the P alignment and enhanced in the AP case depending…
The ultrafast hole dynamics triggered by the photoexcitation of molecular targets is a highly correlated process even for those systems, like organic molecules, having a weakly correlated ground state. We here provide a unifying framework and a numerically efficient matrix formulation of state-of-the-art non-equilibrium Green's function (NEGF) methods like second-Born as well as $GW$ and $T$-matrix without and {\em with} exchange diagrams. Numerical simulations are presented for a paradigmatic, exactly solvable molecular system and the shortcomings of the established NEGF methods are highlight…
We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green's function approximations…
This chapter of "The Oxford Handbook of Nanoscience and Technology: Frontiers and Advances" reviews nonequilibrium Green function (NEGF) approach to modeling spin current generation, transport, and detection in semiconductor nanostructures containing different types of spin-orbit (SO) couplings. Its tutorial style--with examples drawn from the field of the spin Hall effects (SHEs) and with treatment of the Rashba, Dresselhaus and extrinsic SO couplings--offers practical recipes to compute total spin and charge currents flowing out of the device, as well as the nonequilibrium local spin densiti…
We put forward a first-principle NonEquilibrium Green's Function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin samples. The method can deal with pump fields of arbitrary strength, frequency and duration as well as for overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first exper…
We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at $t=0$. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quan…
We study the role of excited phonon populations in the relaxation rates of nonequilibrium electrons using a nonequilibrium Green's function formalism. The transient modifications in the phononic properties are accounted for by self-consistently solving the Dyson equation for the electron and phonon Green's functions. The pump induced changes manifest in both the electronic and phononic spectral functions. We find that the excited phonon populations suppress the decay rates of nonequilibrium electrons due to enhanced phonon absorption. The increased phonon occupation also sets the nonequilibriu…
