Chapter 10 Time-dependent transport phenomena

Nonadiabatic Electron Dynamics in Tunneling Junctions: Lattice Exchange-Correlation Potential

The search for exchange-correlation functionals going beyond the adiabatic approximation has always been a challenging task for time-dependent density-functional theory. Starting from known results and using symmetry properties, we put forward a nonadiabatic exchange-correlation functional for lattice models describing a generic transport setup. We show that this functional reduces to known results for a single quantum dot connected to one or two reservoirs and furthermore yields the adiabatic local-density approximation in the static limit. Finally, we analyze the features of the exchange-correlation potential and the physics it describes in a linear chain connected to two reservoirs where the transport is induced by a bias voltage applied to the reservoirs. We find that the Coulomb blockade is correctly described for a half-filled chain, while additional effects arise as the doping of the chain changes.

Transient Charge and Energy Flow in the Wide-Band Limit

The wide-band limit is a commonly used approximation to analyze transport through nanoscale devices. In this work we investigate its applicability to the study of charge and heat transport through molecular break junctions exposed to voltage biases and temperature gradients. We find by comparative simulations that while the wide-band-limit approximation faithfully describes the long-time charge and heat transport, it fails to characterize the short-time behavior of the junction. In particular, we show that the charge current flowing through the device shows a discontinuity when a temperature gradient is applied, while the energy flow is discontinuous when a voltage bias is switched on and even diverges when the junction is exposed to both a temperature gradient and a voltage bias. We provide an explanation for this pathological behavior and propose two possible solutions to this problem.

Transport through correlated systems with density functional theory

We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-Büttiker(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 the 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 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 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.

Steady-State Density Functional Theory for Finite Bias Conductances

In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.

Electron transport properties of diarylethene photoswitches by a simplified NEGF-DFT approach

A homemade program called FOXY has been used for the theoretical investigation on the conducting properties of two diarylethene based molecules, which, according to recent literature data, can act as photoswitches. FOXY uses a simplified method relying on NEGF theory coupled to DFT calculations and using a suitable electric field to mimic the bias voltage, together with a simple representation of the electrodes. The results confirm the experimental findings and are rationalized by analyzing the space extension of the pertinent molecular orbitals in the ON and OFF electronic states and confirm the FOXY program as a cheap and reliable code to be used in the field of molecular electronics.