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postgraduate thesis: Nonequilibrium Green's functionhierarchical equation of motion method for timedependent quantum transport
Title  Nonequilibrium Green's functionhierarchical equation of motion method for timedependent quantum transport 

Authors  
Advisors  Advisor(s):Chen, G 
Issue Date  2014 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Chen, S. [陈曙光]. (2014). Nonequilibrium Green's functionhierarchical equation of motion method for timedependent quantum transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5312338 
Abstract  The nonequilibrium Green’s functionhierarchical equation of motion (NEGFHEOM) method has been developed to simulate the timedependent electron transport process. The realtime evolution of the reduced singleelectron density matrix is solved through the LiouvillevonNeumann 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 secondtier in the timedependent noninteracting KohnSham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the firsttier. The resulting NEGFHEOMWBL 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 paralinkage or metalinkage 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)NEGFHEOMWBL method is implemented to solve realistic systems in the formalism of timedependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the timedependent electron transport through a CNTbased device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGFHEOMWBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGFHEOMWBL method is more suitable. 
Degree  Doctor of Philosophy 
Subject  Quantum theory  Mathematics Green's functions Transport theory 
Dept/Program  Chemistry 
Persistent Identifier  http://hdl.handle.net/10722/206344 
HKU Library Item ID  b5312338 
DC Field  Value  Language 

dc.contributor.advisor  Chen, G   
dc.contributor.author  Chen, Shuguang   
dc.contributor.author  陈曙光   
dc.date.accessioned  20141023T23:14:28Z   
dc.date.available  20141023T23:14:28Z   
dc.date.issued  2014   
dc.identifier.citation  Chen, S. [陈曙光]. (2014). Nonequilibrium Green's functionhierarchical equation of motion method for timedependent quantum transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5312338   
dc.identifier.uri  http://hdl.handle.net/10722/206344   
dc.description.abstract  The nonequilibrium Green’s functionhierarchical equation of motion (NEGFHEOM) method has been developed to simulate the timedependent electron transport process. The realtime evolution of the reduced singleelectron density matrix is solved through the LiouvillevonNeumann 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 secondtier in the timedependent noninteracting KohnSham framework. When combined with the wide band limit (WBL) approximation, the HEOM terminate at the firsttier. The resulting NEGFHEOMWBL 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 paralinkage or metalinkage 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)NEGFHEOMWBL method is implemented to solve realistic systems in the formalism of timedependent density functional theory (tightbinding). Ab initio calculations are carried out to simulate the timedependent electron transport through a CNTbased device. The simulation results show that when the input bias voltage is in low frequency, both the conventional adiabatic approximation method and the NEGFHEOMWBL methods are good enough. However, when high frequency dynamic responses are need to be captured, the NEGFHEOMWBL method is more suitable.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  Creative Commons: AttributionNonCommerical 3.0 Hong Kong License   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.subject.lcsh  Quantum theory  Mathematics   
dc.subject.lcsh  Green's functions   
dc.subject.lcsh  Transport theory   
dc.title  Nonequilibrium Green's functionhierarchical equation of motion method for timedependent quantum transport   
dc.type  PG_Thesis   
dc.identifier.hkul  b5312338   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Chemistry   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b5312338   