Time-dependent density functional theory for quantum transport

Abstract

Based on our earlier works [Phys. Rev. B 75, 195127 (2007) & J. Chem. Phys. 128, 234703 (2008], we propose a formally exact and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.

Current through a multilead nanojunction in response to an arbitrary time-dependent bias

“…This is a good approximation in systems for which transport takes place at energies close to the Fermi level, and in cases where the matrices α (ω) and α (ω) vary slowly with ω. Detailed ab initio studies of the WBLA in transport calculations reveal that it compares favorably to fully self-consistent simulations for choices of the leads in which the density of states of the metal electrodes (DOS) are approximately constant (for example, bulk gold) [21,51]. However, even in these systems it can lead to error in the estimation of the HOMO-LUMO gap from the transmission coefficient, and miscalculation of splittings in the transmission peaks when a bias is applied.…”

“…In these approaches, the system is prepared in an equilibrium state whose electronic structure is obtained from ab initio calculations, before the time-dependent perturbation is applied [19,21,[49][50][51]. We do not pursue these methods here as they can only be facilitated numerically.…”

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions

“…This method has been successfully employed in simulations of current carrying molecular junctions. [36][37][38] A larger 6-311+ G * basis set is used for the dithiol part, for better description of the charged states. For the doublet anion and cation, calculated states with large spin contaminations were filtered out (a threshold of |⟨S 2 ⟩ − 3/4| > 1.0 was used where 3/4 is the reference value for a doublet state).…”

Transient dynamics in interacting nanojunctions within self-consistent perturbation theory

“…The most interesting and general coherentinteracting regime constitutes a great theoretical challenge. This regime has been addressed using several complementary approaches: diagrammatic techniques [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47], quantum Monte-Carlo (MC) [48][49][50][51][52][53][54][55], timedependent NRG [56][57][58][59][60][61][62][63], time-dependent DFT [64][65][66][67][68][69][70] among others [71][72][73][74][75].However, all of these techniques as they are actually implemented have some limitations. For instance, numerically exact methods like quantum MC are strongly time-consuming, require finite temperature and typically do not allow to reach long time scales.…”