An efficient method for quantum transport simulations in the time domain

Abstract

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In this scheme, the density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab-initio implementations of this formalism, the Hamiltonian is here approximated by a density expansion in the spirit of the density functional based tight-binding (DFTB) method without introducing empirical parameters. Results are presented for two prototypical molecular devices and compared to calculations at the full TDDFT level. The issue of non-existence of a steady state under certain conditions is also briefly touched on.

Higher harmonics and ac transport from time dependent density functional theory

“…Due to the symmetric structure with equal lead-molecule distances on both sides of the device, the I-V characteristic has inversion symmetry around the origin. For low bias the current rises roughly linearly, while around 2 V a steep increase is observed, which arises due to the LUMO 2 of the molecule entering the bias window [35].…”

“…3, a 1,4-benzenediol molecule coupled to an Al nanowire. This junction was already characterized in earlier work [42,35] and the admittance G(ω) has also been computed in Ref. [38].…”

“…At present state, it is numerically extremely expensive to extract information about the admittance behaviour for such demanding systems by use of TD-DFT. Consequently, we employ the above propagation scheme in conjunction with an approximate form of TD-DFT, namely time dependent density functional based tight-binding (TD-DFTB) [33,34,35] in addition to the WBL already mentioned. The Hamiltonian matrix then takes the following form:…”

Time-dependent density functional theory for open systems with a positivity-preserving decomposition scheme for environment spectral functions

“…With the WBL, the ϵ-dependence of Λ α (ϵ) is neglected and a constant reservoir spectral matrix is used. 5,[19][20][21][22][23] Consequently, the resulting numerical procedure is largely simplified. However, the WBL becomes less accurate when the electron dynamics is driven by external fields of large amplitudes or high frequencies.…”

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

“…(a) C. Carbon-chain-benzene-carbon-chain system (DFTB model) 14 Now we turn to the realistic system modeled by the density-functional-based-tight-binding (DFTB) Hamiltonian [27][28]. This model is an approximation of DFT method derived from the second-order expansion of DFT Kohn-Sham energy around the reference charge density.…”