Transport through correlated systems with density functional theory

We present recent advances in Density Functional Theory (DFT) for applications to the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-B\"uttiker(LB)+DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as temperature increases. To overcome the limitations of LB+DFT the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on the one-to-one correspondence between the pair of basic variables steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike in TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.Comment: 29 pages, 22 Figure

Transient dynamics in the Anderson-Holstein model with interfacial screening

We study the combined effects of electron-phonon coupling and dot-lead repulsion in the transport properties of the Anderson-Holstein model. We employ a recently proposed nonperturbative method to calculate the transient response of the system. By varying the initial conditions for the time propagation the current exhibits transient oscillations of different nature. We are able to disentangle two dynamical processes, namely the local charge rearrangement due to the dot-lead contacting and the establishment of the nonequilbrium many-body state due to the application of the external bias. These processes involve either Franck-Condon excitations or transitions between the resonant level and the Fermi energy of the leads.Comment: 6 pages, 6 figure

Dynamical correction to linear Kohn-Sham conductances from static density functional theory

For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculations. The only quantity needed is the static xc potential in the molecular junction. Our scheme provides a comprehensive description of Coulomb blockade without breaking the spin symmetry. This is explicitly demonstrated in single-wall nanotubes where the corrected conductance is in good agreement with experimental data whereas the KS conductance fails dramatically.Comment: 5 pages (4 figures) + 3 pages (2 figures) Supplemental Materia

AC transport in Correlated Quantum Dots: From Kondo to Coulomb blockade regime

We explore the finite bias DC differential conductance of a correlated quantum dot under the influence of an AC field, from the low-temperature Kondo to the finite temperature Coulomb blockade regime. Real-time simulations are performed using a time-dependent generalization of the steady-state density functional theory (i-DFT) [Nano Lett. {\bf 15}, 8020 (2015)]. The numerical simplicity of i-DFT allows for unprecedented long time evolutions. Accurate values of average current and density are obtained by integrating over several periods of the AC field. We find that (i) the zero-temperature Kondo plateau is suppressed, (ii) the photon-assisted conductance peaks are shifted due to correlations and (iii) the Coulomb blockade is lifted with a concomitant smoothening of the sharp diamond edges.Comment: 5 pages, 4 figure

Time-dependent i-DFT exchange-correlation potentials with memory: Applications to the out-of-equilibrium Anderson model

We have recently put forward a steady-state density functional theory (i-DFT) to calculate the transport coefficients of quantum junctions. Within i-DFT it is possible to obtain the steady density on and the steady current through an interacting junction using a fictitious noninteracting junction subject to an effective gate and bias potential. In this work we extend i-DFT to the time domain for the single-impurity Anderson model. By a reverse engineering procedure we extract the exchange-correlation (xc) potential and xc bias at temperatures above the Kondo temperature $T_{\rm K}$. The derivation is based on a generalization of a recent paper by Dittmann et al. [arXiv:1706.04547]. Interestingly the time-dependent (TD) i-DFT potentials depend on the system's history only through the first time-derivative of the density. We perform numerical simulations of the early transient current and investigate the role of the history dependence. We also empirically extend the history-dependent TD i-DFT potentials to temperatures below $T_{\rm K}$. For this purpose we use a recently proposed parametrization of the i-DFT potentials which yields highly accurate results in the steady state.Comment: 7 pages, 4 figure

The dissection algorithm for the second-Born self-energy

We describe an algorithm to efficiently compute the second-Born self-energy of many-body perurbation theory. The core idea consists in dissecting the set of all four-index Coulomb integrals into properly chosen subsets, thus avoiding to loop over those indices for which the Coulomb integrals are zero or negligible. The scaling properties of the algorithm with the number of basis functions is discussed. The computational gain is demonstrated in the case of one-particle Kohn-Sham basis for organic molecules.Comment: 6 pages, contribution to the proceedings of the workshop "Progress in Nonequilibrium Green's Function VII

Missing derivative discontinuity of the exchange-correlation energy for attractive interactions: the charge Kondo effect

We show that the energy functional of ensemble Density Functional Theory (DFT) [Perdew et al., Phys. Rev. Lett. 49, 1691 (1982)] in systems with attractive interactions is a convex function of the fractional particle number N and is given by a series of straight lines joining a subset of ground-state energies. As a consequence the exchange-correlation (XC) potential is not discontinuous for all N. We highlight the importance of this exact result in the ensemble-DFT description of the negative-U Anderson model. In the atomic limit the discontinuity of the XC potential is missing for odd N while for finite hybridizations the discontinuity at even N is broadened. We demonstrate that the inclusion of these properties in any approximate XC potential is crucial to reproduce the characteristic signatures of the charge-Kondo effect in the conductance and charge susceptibility.Comment: 5 pages, 5 eps figure. Phys. Rev. B 86, 081409(R) (2012

CHEERS: A tool for Correlated Hole-Electron Evolution from Real-time Simulations

We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.Comment: 15 pages, 6 figures, to be published, J. Phys.: Condens. Matter (2018

Time-dependent transport in graphene nanoribbons

We theoretically investigate the time-dependent ballistic transport in metallic graphene nanoribbons after the sudden switch-on of a bias voltage $V$. The ribbon is divided in three different regions, namely two semi-infinite graphenic leads and a central part of length $L$, across which the bias drops linearly and where the current is calculated. We show that during the early transient time the system behaves like a graphene bulk under the influence of a uniform electric field $E=V/L$. In the undoped system the current does not grow linearly in time but remarkably reaches a temporary plateau with dc conductivity $\sigma_{1}=\pi e^{2}/2h$, which coincides with the minimal conductivity of two-dimensional graphene. After a time of order $L/v_{F}$ ($v_{F}$ being the Fermi velocity) the current departs from the first plateau and saturates at its final steady state value with conductivity $\sigma_{2}=2e^{2}/h$ typical of metallic nanoribbons of finite width.Comment: 5 pages, 5 figure