Developments in many-body theory of quantum transport and spectroscopy with non-equilibrium Green's functions and time-dependent density functional theory

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

Time-resolved photoabsorption in finite systems : A first-principles NEGF approach

We describe a first-principles NonEquilibrium Green’s Function (NEGF) approach to time-resolved photoabsortion spectroscopy in atomic and nanoscale systems. The method is used to highlight a recently discovered dynamical correlation effect in the spectrum of a Krypton gas subject to a strong ionizing pump pulse. We propose a minimal model that captures the effect, and study the performance of time-local approximations versus time-nonlocal ones. In particular we implement the time-local Hartree-Fock and Markovian second Born (2B) approximation as well as the exact adiabatic approximation within the Time-Dependent Density Functional Theory framework. For the time-nonlocal approximation we instead use the 2B one. We provide enough convincing evidence for the fact that a proper description of the spectrum of an evolving admixture of ionizing atoms requires the simultaneous occurrence of correlation and memory effects.peerReviewe

Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory

We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential Ω[G] regarded as variational functional of the Green’s function G based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger–Ward form. By restricting the input Green’s function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To establish the one-to-one mapping we use that, at any finite temperature and for a given 1RDM γ in a finite basis, there exists a non-interacting system with a spatially non-local potential v[γ] which reproduces the given 1RDM. The corresponding set of non-interacting Green’s functions defines the variational domain of the functional Ω. In the zero temperature limit we obtain an energy functional E[γ] which by minimisation yields an approximate ground state 1RDM and energy. As an application of the formalism we use the Klein and Luttinger–Ward functionals in the GW-approximation to compute the binding curve of a model hydrogen molecule using an extended Hubbard Hamiltonian. We compare further to the case in which we evaluate the functionals on a Hartree–Fock and a Kohn–Sham Green’s function. We find that the Luttinger–Ward version of the functionals performs the best and is able to reproduce energies close to the GW energy which corresponds to the stationary point.peerReviewe