Treatment of time‐dependent effects in molecular junctions

Abstract

The current through molecular junctions can be influenced by various time‐dependent perturbations. Among these are external (laser) fields and fluctuating environments. Both types of external perturbations can lead to large and fast fluctuations of the site energies and electronic couplings involved in the charge transfer. In these cases, theoretical approaches have to be utilized which can accurately and efficiently determine the resulting strongly time‐dependent charge current. To this end we review different formalisms based on the decomposition of the spectral density and the Fermi function, i.e., a standard perturbative approach to second and fourth‐order, a hierarchical theory as well as a nonequilibrium Green's function formalism. The accuracy of the different approaches for the single resonant level model is numerically studied. In an additional test, the electronic level is driven in order to analyze the accuracy for time‐dependent scenarios. Moreover, the results for a multi‐site setup with strongly fluctuating levels are analyzed and compared to a snapshot‐averaged Landauer approach.

Plasmon-enhanced molecular electroluminescence: Effects of nonlinear excitation and molecular cooperativity

“…This value gives the limit up to which the second order molecule-lead coupling approach as used here remains valid (see the recent discussion in Ref. [24]). Considering the variation N pl with (L) gf one notices the maximum around 30 meV.…”

Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments

“…where the stochastic process Z * j (t) = −i λ g * j,λ e iω j,λ t z * j,λ is characterized by its correlation function Besides describing the correlation of the noise process, the bath correlation function also weights the functional derivative at different times under the memory integral in (9). Since this term is non-local in time as well as in the realization of the processes, it is unclear how this term can be evaluated in general.…”

“…The latter property can be used to derive a master equation for the reduced density operator (6). However, no feasible scheme for calculating the Q-operator and, hence, solving the fermionic NMQSD equation (9) has been found so far. Therefore, we will present a different approach in the next section that does not rely on the Q-operator ansatz.…”

“…Therefore, we will present a different approach in the next section that does not rely on the Q-operator ansatz. ‡ Note that the integral boundaries in (9) arise from the specific vacuum initial conditions (5); see [17, Footnote 42] for details.…”

Formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution

“…In order to determine the nonequilibrium dynamics of the double dot system, we employ the hierarchical quantum master equation method [43,66,[69][70][71]. This is an equation of motion technique to determine the reduced density matrix…”