Riku Tuovinen

Time-dependent Landauer-Buttiker formula: application to transient dynamics in graphene nanoribbons

In this work we develop a time-dependent extension of the Landauer-Buttiker approach to study transient dynamics in time-dependent quantum transport through molecular junctions. A key fea- ture of the approach is that it provides a closed integral expression for the time-dependence of the density matrix of the molecular junction after switch-on of a bias in the leads or a perturbation in the junction, which in turn, can be evaluated without the necessity of propagating individual single-particle orbitals or Greens functions. This allows for the study of time-dependent transport in large molecular systems coupled to wide band leads. As an application of the formalism we study the transient dynamics of zigzag and armchair graphene nanoribbons of different symmetries. We find that the transient times can exceed several hundreds of femtoseconds while displaying a long time oscillatory motion related to multiple reflections of the density wave in the nanoribbons at the ribbon-lead interface. This temporal profile has a shape that scales with the length of the ribbons and is modulated by fast oscillations described by intra-ribbon and ribbon-lead transitions. Especially in the armchair nanoribbons there exists a sequence of quasi-stationary states related to reflections at the edge state located at the ribbon-lead interface. In the case of zigzag nanorib- bons there is a predominant oscillation frequency associated with virtual transitions between the edge states and the Fermi levels of the electrode. We further study the local bond currents in the nanoribbons and find that the parity of the edges strongly affects the path of the electrons in the nanoribbons. We finally study the behavior of the transients for various added potential profiles in the nanoribbons.

Image charge dynamics in time-dependent quantum transport

In this work we investigate the effects of the electron-electron interaction between a molecular junction and the metallic leads in time-dependent quantum transport. We employ the recently developed embedded Kadanoff-Baym method [Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction changes substantially the transient and steady-state transport properties. We first show that the mean-field Hartree-Fock (HF) approximation does not capture the polarization effects responsible for the renormalization of the molecular levels neither in nor out of equilibrium. Furthermore, due to the time-local nature of the HF self-energy there exists a region in parameter space for which the system does not relax after the switch-on of a bias voltage. These and other artifacts of the HF approximation disappear when including correlations at the second-Born or GW levels. Both these approximations contain polarization diagrams which correctly account for the screening of the charged molecule. We find that by changing the molecule-lead interaction the ratio between the screening and relaxation time changes, an effect which must be properly taken into account in any realistic time-dependent simulation. Another important finding is that while in equilibrium the molecule-lead interaction is responsible for a reduction of the HOMO-LUMO gap and for a substantial redistribution of the spectral weight between the main spectral peaks and the induced satellite spectrum, in the biased system it can have the opposite effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap.

Time-dependent Landauer-Büttiker formula for transient dynamics

We solve analytically the Kadanoff?Baym equations for a noninteracting junction connected to an arbitrary number of noninteracting wide-band terminals. The initial equilibrium state is properly described by the addition of an imaginary track to the time contour. From the solution we obtain the time-dependent electron densities and currents within the junction. The final results are analytic expressions as a function of time, and therefore no time propagation is needed ? either in transient or in steady-state regimes. We further present and discuss some applications of the obtained formulae.

Phononic heat transport in the transient regime: An analytic solution

We investigate the time-resolved quantum transport properties of phonons in arbitrary harmonic systems connected to phonon baths at different temperatures. We obtain a closed analytic expression of the time-dependent one-particle reduced density matrix by explicitly solving the equations of motion for the nonequilibrium Greens function. This is achieved through a well-controlled approximation of the frequency-dependent bath self-energy. Our result allows for exploring transient oscillations and relaxation times of local heat currents, and correctly reduces to an earlier known result in the steady-state limit. We apply the formalism to atomic chains, and benchmark the validity of the approximation against full numerical solutions of the bosonic Kadanoff-Baym equations for the Greens function. We find good agreement between the analytic and numerical solutions for weak contacts and baths with a wide energy dispersion. We further analyze relaxation times from low to high temperature gradients.