Nonequilibrium Green's function-hierarchical equation of motion method for time-dependent quantum transport

Abstract

The nonequilibrium Green’s function-hierarchical equation of motion (NEGFHEOM) method has been developed to simulate the time-dependent electron transport process. The real-time evolution of the reduced single-electron density matrix is solved through the Liouville-von-Neumann equation. The method is very efficient compared to conventional NEGF formulas which need to discretize the simulation time. The hierarchical equation of motion (HEOM) is closed at the second-tier in the time-dependent noninteracting Kohn-Sham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the first-tier. The resulting NEGF-HEOM-WBL method is particularly suitable for simulating the long time transient dynamics for large systems.

The method developed is first applied to calculate the transient current through an array of as many as 1000 quantum dots. Upon switching on the bias voltage, the current increases linearly with respect to time before reaching its steady state value. And the time required for the current to reach its steady state value is exactly the time for a conducting electron to travel through the array at Fermi velocity. These phenomena can be understood by simple analysis on the energetics of the quantum dots or by classical electron gas model.

Then the method is employed to investigate several simple molecular circuits, in which the para-linkage or meta-linkage benzene acts as the transmitting molecular entity. The simulation results shows that it takes a certain amount of time before the quantum interference manifests itself, and that the transmission through the meta case is hundreds of times smaller than that through the para case. To investigate the quantum interference process in molecular electronics, the concept of Büttiker probe is introduced. The Büttiker probe is an electrode that, when attached to electronic devices, causes the coherence passing through disappear. Simulation results show that the Büttiker probe can enhance the transmission of the meta benzene system through destroying the constructive interference. By turning the probe on and off, it can be observed that large strong correlations are indeed built up as electrons are transported through benzenoid structures - when the decoherence is turned off, the current rises, and when the decoherence is turned back on, the current falls.

Finally, TDDFT(B)-NEGF-HEOM-WBL method is implemented to solve realistic systems in the formalism of time-dependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the time-dependent electron transport through a CNT-based device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGF-HEOM-WBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGF-HEOM-WBL method is more suitable.