We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems ( Phys. Rev. Lett. , 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.
We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems ( Phys. Rev. Lett. , 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.
We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time dependence of these observables provides a wealth of information on the energy level structure of the quantum wire out of equilibrium. For moderate interaction strengths the second Born and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias-dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.
Full understanding of the relaxation mechanisms and far-from-equilibrium transport in modern mesoscopic structures requires that such systems be treated as open. We therefore generalize some of the core elements of the Kadanoff-Baym-Keldysh nonequilibrium Green's function formalism, inherently formulated for closed systems, to treatment of an open system, coupled with its environment. We define the two-time correlation functions and analyze the influence of the memory effects on the open-system transport. In the transient regime, the two-time correlation functions clearly show four distinct terms: a closed-system-like term, an entanglement term, and two memory terms that depend explicitly on the initial state of the environment. We show that it is not possible to completely eliminate the influence of the environment by a fortunate choice of the initial state, and approximating the system as closed is valid only in the limit of negligible system-environment coupling, which is never the case in the transient regime. We derive the transport equations for transients that properly account for the system-environment coupling. On the other hand, we address the important issue of transport in a far-from-equilibrium steady state. We show that, once a steady state is reached, the balance between the driving and relaxation forces implies that the two-time correlation functions regain a closed-system-like form, but with an effective, modified system Hamiltonian, and with the system statistical operator unrelated to that of the initial state. We emphasize that the difference between the transient and the far-from-equilibrium steady-state regimes, crucial for theoretical investigation of nonequilibrium quasiparticle transport, effectively lies within the different relative magnitude of the combined entanglement and memory terms with respect to the closed-system-like term in two-time correlation functions.
We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an "embedding correlator" from which the time-dependent current can be calculated using the Meir-Wingreen formula. We show how to efficiently implement our approach through a simple grafting into recently proposed time-linear Green's function methods for closed systems. Electron-electron and electron-phonon interactions can be treated on equal footing while preserving all fundamental conservation laws.
In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.
We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.
We discuss a nonequilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical fluctuations. The theory reduces to nonequilibrium dynamical mean-field theory in the presence of only electron-electron interactions and to the coherent potential approximation in noninteracting systems with disorders. Both time-dependent and steady-state problems are treated by implementing the theory on the three-branch Kadanoff-Baym contour and two-branch Schwinger-Keldysh contour, respectively. Benchmarks on a eight-site cube show that the method yields rather accurate spectral functions in both the weakly and strongly interacting regimes. In a cubic lattice, we demonstrate energy conservation after an interaction quench and thermalization after just a few hopping times in both clean and disordered systems. As an application, we study transport through a serial double quantum-dot sandwiched between two leads, focusing on the current and dot occupations after a voltage quench.