We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined by real-time propagation of the Kadanoff-Baym equations after applying a bias voltage to the system. The electronic interactions on the central site are incorporated by means of self-energy approximations at Hartree-Fock, second Born and GW level. We investigate the conditions under which multiple steady-state solutions occur within different self-energy approximations, and analyze in detail the nature of these states from an analysis of their spectral functions. At the Hartree-Fock level at least two stable steady-state solutions with different densities and currents can be found. By applying a gate voltage-pulse at a given time we are able to switch between these solutions. With the same parameters we find only one steady-state solution when the self-consistent second Born and GW approximations are considered. We therefore conclude that treatment of many-body interactions beyond mean-field can destroy bistability and lead to qualitatively different results as compared those at mean-field level.
We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined by real-time propagation of the Kadanoff-Baym equations after applying a bias voltage to the system. The electronic interactions on the central site are incorporated by means of self-energy approximations at Hartree-Fock, second Born and GW level. We investigate the conditions under which multiple steady-state solutions occur within different self-energy approximations, and analyze in detail the nature of these states from an analysis of their spectral functions. At the Hartree-Fock level at least two stable steady-state solutions with different densities and currents can be found. By applying a gate voltage-pulse at a given time we are able to switch between these solutions. With the same parameters we find only one steady-state solution when the self-consistent second Born and GW approximations are considered. We therefore conclude that treatment of many-body interactions beyond mean-field can destroy bistability and lead to qualitatively different results as compared those at mean-field level.
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.
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 present in detail a method we recently introduced (PRL. 103, 176404 (2009)) to describe finite systems in and out of equilibrium, where the evolution in time is performed via the Kadanoff-Baym Equations (KBE) within Many-Body Perturbation Theory (MBPT). The main property we analyze is the time-dependent density. We also study is the exchange-correlation potential of TDDFT, obtained via reverse engineering from the time-dependent density. Our systems consist of small, strongly correlated clusters, described by a Hubbard Hamiltonian within the Hartree-Fock, second Born, GW and T-matrix approximations. We compare the results from the KBE dynamics to those from exact numerical solutions. The outcome of our comparisons is that, among the many-body schemes considered, the T-matrix approximation is overall superior at all electron densities. Such comparisons permit a general assessment of the whole idea of applying MBPT, in the KBE sense, to finite systems. A striking outcome of our analysis is that when the system evolves under a strong external field, the KBE develop a steady-state solution as a consequence of a correlation-induced damping. This damping is present both in isolated (finite) systems, where it is purely artificial, as well as in clusters contacted to (infinite) macroscopic leads. To illustrate this point we present selected results for a system coupled to contacts within the T-matrix and second Born approximation. The extensive characterization we performed indicates that this behavior is present whenever approximate self energies, based upon infinite partial summations, are used. A second important result is that, for isolated clusters, the steady state reached is not unique but depends on how one switches on the external field. This may also true for clusters connected to leads.
We present in detail a method we recently introduced [Phys. Rev. Lett. 103, 176404 (2009)] to describe finite systems in and out of equilibrium, where the evolution in time is performed via the Kadanoff-Baym equations within many-body perturbation theory. Our systems consist of small, strongly correlated clusters, described by a Hubbard Hamiltonian within the Hartree-Fock, second Born, GW, and T-matrix approximations. We compare the results from the Kadanoff-Baym dynamics to those from exact numerical solutions. The outcome of our comparisons is that, among the many-body schemes considered, the T-matrix approximation is superior at low electron densities while none of the tested approximations stands out at half filling. Such comparisons permit a general assessment of the whole idea of applying many-body perturbation theory, in the Kadanoff-Baym sense, to finite systems. A striking outcome of our analysis is that when the system evolves under a strong external field, the Kadanoff-Baym equations develop a steady-state solution as a consequence of a correlation-induced damping. This damping is present both in isolated (finite) systems, where it is purely artificial, as well as in clusters contacted to (infinite) macroscopic leads. The extensive numerical characterization we performed indicates that this behavior is present whenever approximate self-energies, which include correlation effects, are used. Another important result is that, for isolated clusters, the steady state reached is not unique but depends on how one switches on the external field. When the clusters are coupled to macroscopic leads, one may reach multiple quasisteady states with arbitrarily long lifetimes.
We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-matrix levels as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-ansatz local density approximation (ABALDA) for the exchange-correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads, and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG, especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site, but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities, which indicates that the exchange-correlation potential must attain nonzero values in the leads.
The problem of quantum dynamics in open systems has gained attention in recent decades and not the least due to the advances made in quantum transport in molecular systems. The main motivation behind quantum transport and molecular electronics is the futuristic goal to be able at some point to replace, or to complement, the silicon-based technology and to make the electronic devices faster. On a fundamental level, one has to deal with time-dependent processes where electron-electron or electron- phonon interactions are of great importance, and they can cause profound quantitative and qualitative changes on the physical and dynamical properties of electronic systems compared to the non-interacting case. Most of the studies of quantum transport have been focused on the steady-state description while neglecting the short-time dynamics. However, the dynamical effects are of great importance since fast- switching processes play a pivotal role in the operation of future devices. We studied the problem of time-dependent electron transport through the Anderson impurity model by using many-body perturbation theory (MBPT) together with Keldysh Green’s functions as well as with time-dependent density functional theory (TDDFT). These methods were compared with numerically exact time-dependent density-matrix renormalization group (tDMRG) method. We found that the many-body perturbation theory results beyond Hartree-Fock approximation were in close agreement with tDMRG results. In addition we studied the possibility of multistablity in the density and current of an interacting nanoscale junction as well as how to reversibly switch between the multiple solutions in time domain. An accurate theoretical treatment of electron correlation even in as simple model as an interacting electron gas at metallic densities still continues to be a challenge; especially description of features in the photoemission spectra due to electron correlations provides a theoretical challenge. The many-body perturbation theory yields a systematic way to study electron-electron (electron-phonon) correlations in various systems. One of the widely used approximations in MBPT is the GW approximation in which the bare interaction line is replaced with screened interaction line in the first order exchange diagram. The GW approximation gives good estimates for the band gap values close to experimental ones but especially the self-consistent GW approximation has a number of deficiencies like washing out of plasmon features and overestimation of bandwidths compared to experiment. One way to improve GW calculations is to include vertex corrections. Unfortunately, the straightforward inclusion of vertex corrections yields negative spectra in some frequency regions. We developed a diagrammatic approach to construct self-energy approximations with positive spectral properties. Our approach consists of expressing a self-energy of response diagram as a product of half-diagrams after which a minimal set of additional diagrams is identified to construct a perfect square. We applied this method to study vertex corrections in a homogeneous electron gas. In addition we analyzed the diagrammatic content of photocurrent with density functional theory. The expression for the photocurrent was obtained as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange correlation kernel of current density functional theory. The expression for the photocurrent gives us the angular dependence of the photocurrent but it does not provide a direct access to the kinetic energy distribution of the photoelectrons.