Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects

We study time-dependent quantum transport in a correlated model system by means of time-propagation 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.Comment: 5 pages, 2 figure

Wick Theorem for General Initial States

We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated 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.Comment: 9 pages, 5 figure; extended version published in Phys. Rev.

Classical Nuclear Motion in Quantum Transport

An ab initio quantum-classical mixed scheme for the time evolution of electrode-device-electrode systems is introduced to study nuclear dynamics in quantum transport. Two model systems are discussed to illustrate the method. Our results provide the first example of current-induced molecular desorption as obtained from a full time-dependent approach and suggest the use of ac biases as a way to tailor electromigration. They also show the importance of non-adiabatic effects for ultrafast phenomena in nanodevices.Comment: 5 pages, 3 figure

Charge separation in donor-C60 complexes with real-time Green's functions: The importance of nonlocal correlations

We use the Nonequilibrium Green's Function (NEGF) method to perform real-time simulations of the ultrafast electron dynamics of photoexcited donor-C60 complexes modeled by a Pariser-Parr-Pople Hamiltonian. The NEGF results are compared to mean-field Hartree-Fock (HF) calculations to disentangle the role of correlations. Initial benchmarking against numerically highly accurate time-dependent Density Matrix Renormalization Group calculations verifies the accuracy of NEGF. We then find that charge-transfer (CT) excitons partially decay into charge separated (CS) states if dynamical non-local correlation corrections are included. This CS process occurs in ~10 fs after photoexcitation. In contrast, the probability of exciton recombination is almost 100% in HF simulations. These results are largely unaffected by nuclear vibrations; the latter become however essential whenever level misalignment hinders the CT process. The robust nature of our findings indicate that ultrafast CS driven by correlation-induced decoherence may occur in many organic nanoscale systems, but it will only be correctly predicted by theoretical treatments that include time-nonlocal correlations.Comment: 9 pages, 6 figures + supplemental information (4 pages)

Time-dependent quantum transport: an exact formulation based on TDDFT

An exact theoretical framework based on Time Dependent Density Functional Theory (TDDFT) is proposed in order to deal with the time-dependent quantum transport in fully interacting systems. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external electric field is switched on. Our theory includes the interactions between the leads and between the leads and the device. It is well suited for calculating measurable transient phenomena as well as a.c. and other time-dependent responses. We show that the steady-state current results from a \textit{dephasing mechanism} provided the leads are macroscopic and the device is finite. In the d.c. case, we obtain a Landauer-like formula when the effective potential of TDDFT is uniform deep inside the electrodes.Comment: final version, 7 pages, 1 figur

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 nano-scale 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 non-interacting Kohn-Sham (KS) system under the influence of different Peierls phases {\em and} of a pairing field. An extended Keldysh formalism for the non-equilibrium Nambu-Green's function (NEGF) 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-deGennes (BdG) equations is shown. For systems consisting of a finite region coupled to ${\cal N}$ superconducting semi-infinite leads we numerically solve the static BdG equations with a generalized wave-guide 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.Comment: 20 pages, 9 figures, published versio

Plunging into the pool of death: Imagining a dangerous outcome influences distance perception

We examined whether manipulating the imagined consequences of falling would influence the perception of height, distance, and size. In experiment I, height and size perception were measured When participants stood at a short height (0.89 m) or a medium height (1.91 m) above either an empty pool or a pool filled with a bed of nails. Participants who viewed the bed of nails and imagined falling into it estimated both the height as taller and the size of the bed of nails as larger than participants who imagined falling into an empty pool. In a second experiment, participants overestimated the horizontal ground distance to and across the bed of nails after being told to imagine jumping over it. Overall, these experiments suggest that costs associated with imagined actions can influence the perception of both vertical and horizontal extents that are not inherently dangerous

Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems

Correlation effects in bistability at the nanoscale: steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure

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

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.Comment: 16 pages, 9 figures. Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc