In this work we develop a time-dependent extension of the Landauer-Büttiker approach to study transient dynamics in time-dependent quantum transport through molecular junctions. A key feature 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 Green's 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 nanoribbons 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.
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. Assumptions and set-upWe investigate the following quantum transport setup: An arbitrary number of metallic leads (α) acting as charge-carrier reservoirs are connected to a lattice network acting as a molecular device (C). We assume that the electron transport is ballistic and therefore neglect the electronelectron interactions. We will also assume that the energy eigenvalues of the Hamiltonian of the molecular device are well inside the continuous energy spectrum of the leads and use the WBLA.The described set-up is characterized by the following Hamiltonian:The first term accounts for the leads with kα indexing the k:th basis function of the α = 1, 2, 3, . . .
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.
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.
A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff-Baym Ansatz (GKBA) is applied to a lattice system with a symmetry-broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetrybroken initial state from a Hartree-Fock wave function within GKBA is assessed by comparing with a solution of the imaginary-time Dyson equation. It is found that it is possible to reach a symmetry-broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.
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