Gianluca Stefanucci

A many-body approach to quantum transport dynamics: Initial correlations and memory effects

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 Greens 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 in a correlated model system by means of timepropagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green function. We consider an initially contacted equilibrium system of a correlated central region coupled to tight-binding leads. Subsequently a time-dependent bias is switched on after which we follow in detail the time-evolution of the system. Important features of the Kadanoff-Baym approach are 1) the possibility of studying 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 find that initial correlation and memory terms due to many-body interactions have a large effect on the transient currents. Furthermore the value of the steady state current is found to be strongly dependent on the approximation used to treat the electronic interactions.

Time-dependent quantum transport with superconducting leads: A discrete-basis Kohn-Sham formulation and propagation scheme

In this work we put forward an exact one-particle framework to study nanoscale Josephson junctions out of equilibrium and propose a propagation scheme to calculate the time-dependent current in response to an external applied bias. Using a discrete basis set and Peierls phases for the electromagnetic field, we prove that the current and pairing densities in a superconducting system of interacting electrons can be reproduced in a noninteracting Kohn-Sham sKS d system under the influence of different Peierls phases and of a pairing field. In the special case of normal systems, our result provides a formulation of time-dependent current-densityfunctional theory in tight-binding models. An extended Keldysh formalism for the nonequilibrium NambuGreen’s function sNEGF d is then introduced to calculate the short- and long-time response of the KS system. The equivalence between the NEGF approach and a combination of the static and time-dependent Bogoliubov-de Gennes sBdG d equations is shown. For systems consisting of a finite region coupled to N superconducting semi-infinite leads, we numerically solve the static BdG equations with a generalized waveguide approach and their time-dependent version with an embedded Crank-Nicholson scheme. To demonstrate the feasibility of the propagation scheme, we study two paradigmatic models, the single-level quantum dot and a tight-binding chain, under dc, ac, and pulse biases. We provide a time-dependent picture of single and multiple Andreev reflections, show that Andreev bound states can be exploited to generate a zero-bias ac current of tunable frequency, and find a long-living resonant effect induced by microwave irradiation of appropriate frequency.

Charge dynamics in molecular junctions: Nonequilibrium Green's function approach made fast

Real-time Greens 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 Greens 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 systems and then construct a suitable quasiparticle propagator that includes correlation effects in a diagrammatic fashion. We also provide evidence that our GKBA scheme, although already in good agreement with the KBE approach, can be further improved without increasing the computational cost.

Ultrafast manipulation of electron spins in a double quantum dot device: A real-time numerical and analytical study

We consider a double single-level quantum dot system with two embedded and nonaligned spin impurities to manipulate the magnitude and polarization of the electron-spin density. The device is attached to semi-infinite one-dimensional leads which are treated exactly. We provide a real-time description of the electron-spin dynamics when a sequence of ultrafast voltage pulses acts on the device. The numerical simulations are carried out using a spin-generalized modified version of a recently proposed algorithm for the time propagation of open systems [Kurth et al., Phys. Rev. B 72, 035308 (2005)]. Time-dependent spin accumulations and spin currents are calculated during the entire operating regime, which includes spin-injection and read-out processes. The full knowledge of the electron dynamics allows us to engineer the transient responses and improve the device performance. An approximate rate equation for the electron spin is also derived and used to discuss the numerical results.

First-principles nonequilibrium Green's-function approach to transient photoabsorption: Application to atoms

We put forward a first-principle nonequilibrium Green’s-function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin systems. The method can deal with pump fields of arbitrary strength, frequency, and duration as well as 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 experiment we explain the bending of the Autler-Townes absorption peaks with increasing pump-probe delay τ and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of dynamical correlation effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of Kr 2+ with respect to Kr 1+ as a function of τ.

Generalized waveguide approach to tight-binding wires: Understanding large vortex currents in quantum rings

We generalize the quantum waveguide approach to Huckel or tight-binding models relevant to unsaturated

Wick Theorem for General Initial States

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Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas

molecular devices. A Landauer-type formula for the current density through internal bonds is also derived which allows for defining a local conductance. The approach is employed to study internal circular currents in two-terminal rings. We show how to predict the occurrence and the nature of large vortex currents in coincidence with vanishingly small currents in the leads. We also prove a remarkably simple formula for the onset of a vortex regime.

Correlation-induced memory effects in transport properties of low-dimensional systems.

We present a compact and simplified proof of a generalized Wick theorem to calculate the Green’s function of bosonicandfermionicsystemsinanarbitraryinitialstate.Itisshownthatthedecompositionofthenoninteracting n-particle Green’s function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for noncorrelated initial states, a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams, and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-step procedure: We first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green’s functions, whereas those of the other half are anti-time-ordered Green’s functions, and the lines joining the two halves are either lesser or greater Green’s functions. The theory is developed using noninteracting Green’s functions and subsequently extended to self-consistent Green’s functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte Carlo momentum integrations to evaluate the diagrams.