Steady-state Density Functional Theory Research Articles

Thermoelectric efficiency in multiterminal quantum thermal machines from steady-state density functional theory

The multi-terminal generalization of the steady-state density functional theory for the description of electronic and thermal transport (iq-DFT) is presented. The linear response regime of the framework is developed leading to exact expressions for the many-body transport coefficients and thermoelectric efficiency purely in terms of quantities accessible to the framework. The theory is applied to a multi-terminal interacting quantum dot in the Coulomb blockade regime for which accurate parametrizations of the exchange-correlation kernel matrix are given. The thermoelectric efficiency and output power of the multi-terminal system are studied. Surprisingly, the strong-interaction limit of these quantities can be understood in terms of the non-interacting one.

Prominent nonequilibrium effects beyond the standard first-principles approach in nanoscale electronic devices.

The standard density functional theory (DFT) based first-principles approach has been widely used for modeling nanoscale electronic devices. A recent experiment, however, reported surprising transport properties of thiol-terminated silane junctions that cannot be understood using the standard DFT approach, presenting a severe challenge for the current computational understanding of electron transport at the nanoscale. Using the recently proposed steady-state DFT (SS-DFT) for nonequilibrium quantum systems, we found that in silane junctions, underlying the puzzling experimental observations is a novel type of intriguing nonequilibrium effect that is beyond the framework of the standard DFT approach. Our calculations show that the standard DFT approach is a good approximation of SS-DFT when silane junctions are near equilibrium, but the aforementioned nonequilibrium effects could drive the thiol-terminated silanes far away from equilibrium even at low biases of around 0.2 V. Further analysis suggests that these nonequilibrium effects could generally exist in nanoscale devices in which there are conducting channels mainly residing at the source contact and close to the bias window. These findings significantly broaden our fundamental understanding of electron transport at the nanoscale.

Mott Metal-Insulator Transition from Steady-State Density Functional Theory.

We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.

Steady-state density functional theory for thermoelectric effects

The recently proposed density functional theory for steady-state transport (i-DFT) is extended to include temperature gradients between the leads. Within this framework, a general and exact expression is derived for the linear Seebeck coefficient which can be written as the sum of the Kohn-Sham coefficient and an exchange-correlation contribution. The formalism is applied to the single-impurity Anderson model for which approximate exchange-correlation functionals are suggested for temperatures both above and below the Kondo temperature. A certain structural property of the exchange-correlation potentials in the Coulomb blockade regime allows to recover an earlier result expressing the Seebeck coefficient in terms of quantities of equilibrium density functional theory. The numerical i-DFT results are compared to calculations with the numerical renormalization group over a wide range of temperatures finding a reasonable agreement while i-DFT comes at a much lower computational cost.

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.

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 TK. The derivation is based on a generalization of a recent paper by Dittmann et al. [N. Dittmann et al., Phys. Rev. Lett. 120, 157701 (2018)]. 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 TK. For this purpose we use a recently proposed parametrization of the i-DFT potentials which yields highly accurate results in the steady state.

Many-Body Spectral Functions from Steady State Density Functional Theory.

We propose a scheme to extract the many-body spectral function of an interacting many-electron system from an equilibrium density functional theory (DFT) calculation. To this end we devise an ideal scanning tunneling microscope (STM) setup and employ the recently proposed steady-state DFT formalism (i-DFT) which allows one to calculate the steady current through a nanoscopic region coupled to two biased electrodes. In our setup, one of the electrodes serves as a probe ("STM tip"), which is weakly coupled to the system we want to measure. In the ideal STM limit of vanishing coupling to the tip, the system is restored to quasi-equilibrium and the normalized differential conductance yields the exact equilibrium many-body spectral function. Calculating this quantity from i-DFT, we derive an exact relation expressing the interacting spectral function in terms of the Kohn-Sham one. As illustrative examples, we apply our scheme to calculate the spectral functions of two nontrivial model systems, namely the single Anderson impurity model and the Constant Interaction Model.

Spin-dependent electron transport through a Mn-phthalocyanine molecule — A steady-state density functional theory (SS-DFT) study

We generalize the recently proposed steady-state density functional theory (SS-DFT) to spin-dependent cases and theoretically investigate the electronic and transport properties of a Mn-phthalocyanine molecule sandwiched between two graphene nanoribbon leads. The junction filters spin-up (minority spin) electrons while allowing spin-down (majority spin) electrons to pass with a filtering efficiency of about 99.5% at low biases. The spin-down electrons are found to tunnel through the junction via the HOMO orbital of the Mn-phthalocyanine molecule. Detailed analysis of the spin-dependent electron tunneling mechanism as well as the electronic/magnetic properties of the junction is presented.

Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions.

We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case.