Time-dependent density functional theory for quantum transport

Abstract

Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous 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.

Correlation effects in bistability at the nanoscale: Steady state and beyond

“…[20][21][22][23][24][25][26][27][28][29][31][32][33][34] We first solve the steady-state equations of DFT and mean-field theory to determine the parameter range for bistability. Then we go beyond the current state-of-the-art and provide a TD description of the bistability phenomenon in adiabatic TDDFT [23][24][25][26][27][28][29] and TD mean-field theory. We show how to switch between different stable states by means of ultrafast gate voltages or external biases (driving fields).…”

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

“…From the figure we see that there exist large oscillations in the beginning, which is the over-shotting effect. This is due to the very narrow spectrum of the lead [16]: Only a small amount of electron near the Fermil level can be disspated into the GNR lead, so most of the electron wave 13 injected in the device is reflected on the device-lead boundary, which gives the oscillation current.…”

“…We opt for another method. Instead of solving the EOM of the Green's functions, new matrices are defined as follows: [13] and [14]. These differential equations constitute a closed set of hierarchical equations, which is exact and solvable.…”

“…In TDDFT-NEGF theory, the lesser self-energy at the equilibrium state is expressed as follows [13][14]: …”

“…Recently we developed a new method to calculate the time dependent quantum transport based on the NEGF theory [13][14][15][16][17]. This method, termed as the time dependent density functional theory -nonequilibrium Green's function (TDDFT-NEGF) scheme, treats the lead spectrum exactly, which is beyond the commonly used wide band limit (WBL) approximation [8][9].…”