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postgraduate thesis: Timedependent quantum transport : first principles simulations and applications
Title  Timedependent quantum transport : first principles simulations and applications 

Authors  
Issue Date  2016 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Kwok, Y. [郭昕豪]. (2016). Timedependent quantum transport : first principles simulations and applications. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  Based on the time dependent density functional theory (TDDFT) for open system and the nonequilibrium Green's function (NEGF) formalism,
a practical first principle method to simulate time dependent quantum transport is developed and applied to different areas.
The method propagates a closed set of equations of motion of the reduced single electron density matrix(RSDM)
and the auxiliary single electron density matrices(ARSDM), which describe the dissipation of the system.
The method can go beyond the commonly used wideband limit approximation and take into account electronic structures of the electrodes accurately.
Nonorthogonal basis, which is commonly used in first principle simulation, is also considered properly.
And in order to make larger scale simulation possible,
two distributedmemory parallelization schemes, the columnwise and checkerboard decomposition schemes, are developed.
They distribute the second tier ARSDM over compute nodes
and the communication involved is basically the same as that in matrix vector multiplication.
So the scalability of the parallelization is also as good as the corresponding schemes in the matrix vector multiplication.
The method is then applied to different areas,
which include the study of timedependent properties in integer quantum hall system and twodimensional electronic spectroscopy in molecular junctions.
Integer quantum hall system is twodimensional metallic system under strong magnetic field.
The system is described by a tight binding Hamiltonian and the magnetic field is taken into account by Peierls substitution.
It is observed that the size of the square lattice would affect the magnetic field strength required to enter the quantum hall regime
and localization of edge current is related to the quantum hall conductance.
The development of current upon applying voltages is also studied for both twoterminal and fourterminal cases.
Finally, we observe how the integer quantum hall system transit from one quantum hall plateau to another by applying a gate voltage in the device region.
For twodimensional electronic spectroscopy (2DES), the method is first benchmarked with simple twolevel and threelevel model systems connected to two wide band electrodes.
We observe peaks resulting from diagrams in which the system is started at excited state.
These peaks are present due to the broadening introduced by the electrodes and they distinguishes 2DES of molecular junctions from 2DES of isolated molecules.
When bias voltage is applied, the changes in occupation number also lead to suppression or enhancement of certain peaks.
Finally, the 2D electronic spectrum of a benzene connected to gold chain electrodes is simulated at density functional tightbinding level with wide band approximation.
The broadening introduced by the gold chain electrodes is pretty small and the electronic spectrum is similar to the isolated benzene.
And when bias voltage is applied, we observe peak shift of the electronic spectrum due to the induced electric field in the device region. 
Degree  Doctor of Philosophy 
Subject  Quantum theory  Mathematics Transport theory 
Dept/Program  Chemistry 
Persistent Identifier  http://hdl.handle.net/10722/239947 
HKU Library Item ID  b5846382 
DC Field  Value  Language 

dc.contributor.author  Kwok, Yanho   
dc.contributor.author  郭昕豪   
dc.date.accessioned  20170408T23:13:15Z   
dc.date.available  20170408T23:13:15Z   
dc.date.issued  2016   
dc.identifier.citation  Kwok, Y. [郭昕豪]. (2016). Timedependent quantum transport : first principles simulations and applications. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/239947   
dc.description.abstract  Based on the time dependent density functional theory (TDDFT) for open system and the nonequilibrium Green's function (NEGF) formalism, a practical first principle method to simulate time dependent quantum transport is developed and applied to different areas. The method propagates a closed set of equations of motion of the reduced single electron density matrix(RSDM) and the auxiliary single electron density matrices(ARSDM), which describe the dissipation of the system. The method can go beyond the commonly used wideband limit approximation and take into account electronic structures of the electrodes accurately. Nonorthogonal basis, which is commonly used in first principle simulation, is also considered properly. And in order to make larger scale simulation possible, two distributedmemory parallelization schemes, the columnwise and checkerboard decomposition schemes, are developed. They distribute the second tier ARSDM over compute nodes and the communication involved is basically the same as that in matrix vector multiplication. So the scalability of the parallelization is also as good as the corresponding schemes in the matrix vector multiplication. The method is then applied to different areas, which include the study of timedependent properties in integer quantum hall system and twodimensional electronic spectroscopy in molecular junctions. Integer quantum hall system is twodimensional metallic system under strong magnetic field. The system is described by a tight binding Hamiltonian and the magnetic field is taken into account by Peierls substitution. It is observed that the size of the square lattice would affect the magnetic field strength required to enter the quantum hall regime and localization of edge current is related to the quantum hall conductance. The development of current upon applying voltages is also studied for both twoterminal and fourterminal cases. Finally, we observe how the integer quantum hall system transit from one quantum hall plateau to another by applying a gate voltage in the device region. For twodimensional electronic spectroscopy (2DES), the method is first benchmarked with simple twolevel and threelevel model systems connected to two wide band electrodes. We observe peaks resulting from diagrams in which the system is started at excited state. These peaks are present due to the broadening introduced by the electrodes and they distinguishes 2DES of molecular junctions from 2DES of isolated molecules. When bias voltage is applied, the changes in occupation number also lead to suppression or enhancement of certain peaks. Finally, the 2D electronic spectrum of a benzene connected to gold chain electrodes is simulated at density functional tightbinding level with wide band approximation. The broadening introduced by the gold chain electrodes is pretty small and the electronic spectrum is similar to the isolated benzene. And when bias voltage is applied, we observe peak shift of the electronic spectrum due to the induced electric field in the device region.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Quantum theory  Mathematics   
dc.subject.lcsh  Transport theory   
dc.title  Timedependent quantum transport : first principles simulations and applications   
dc.type  PG_Thesis   
dc.identifier.hkul  b5846382   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Chemistry   
dc.description.nature  published_or_final_version   