Parameter-free driven Liouville-von Neumann approach for time-dependent electronic transport simulations in open quantum systems

Abstract

Abstract:A parameter free version of the recently developed driven Liouville-von Neumann equation [J. Chem. Theo. Comp. 10, 2927-2941] for electronic transport calculations in molecular junctions is presented. A single driving rate, appearing as a fitting parameter in the original methodology, is replaced by a set of state-dependent broadening factors applied to the different single-particle lead levels. These broadening factors are extracted explicitly from the self-energy of the corresponding electronic reservoir and are fully transferable to any junction incorporating the same lead model. 2

Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations

“…1, captures well the short-time (γt < γ (h∆ε −1 ) = 20π, reflecting the highest frequency of the lead dynamics) exponential decay predicted by the analytical treatment. However, at longer timescales, characteristic Poincaré recurrences occur, reflecting the discrete nature of the quasi-continuum representation of the lead or, equivalently, the reflection of the scattered electron wavefunction from the far edge of the finite lead model [46,39,53,54,55,45]. Therefore, similar to previous multi-lead microcanonical transport calculations [16,36,42], it becomes evident that, while microcanonical simulations are not limited to the WBA, the finite closed system model can mimic the behavior of its open counterpart only for times shorter than the typical reflection time-scale.…”

Lead geometry and transport statistics in molecular junctions

“…It is straightforward to generalize this to more complex models than that used here; for example, analogous procedures for time-dependent noninteracting transport and in the presence of secondary Markovian leads have been discussed in detail in the literature. 25,[113][114][115][116] We begin by rewriting Eq. 5 in terms of Green's functions:…”

Communication: Relaxation-limited electronic currents in extended reservoir simulations

“…(4). For H ℒ and H ℛ separately diagonalized, the self-energies are $${\sum }_{\mathit{\text{ij}}}^{ℒ}=-\frac{i}{2}\sum _{k\in ℒ}{\gamma }_k{\delta }_{\mathit{\text{ij}}}{\delta }_{\mathit{\text{ik}}}{\sum }_{\mathit{\text{ij}}}^{ℛ}=-\frac{i}{2}\sum _{k\in ℛ}{\gamma }_k{\delta }_{\mathit{\text{ij}}}{\delta }_{\mathit{\text{ik}}},$$where γ is nonuniform 2,25,26 . These are matrices on the whole ℒ𝒮ℛ system, but are zero when i or j are outside the respective reservoir region.…”