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postgraduate thesis: Full-counting statistics of charge and spin transport

TitleFull-counting statistics of charge and spin transport
Authors
Issue Date2016
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Tang, G. [唐高民]. (2016). Full-counting statistics of charge and spin transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.
AbstractThis thesis investigates the full-counting statistics (FCS) of charge and spin transport using nonequilibrium Green's function (NEGF) in non-interacting systems. Generating function (GF) encodes all the distribution information and is the key of FCS. For the charge statistics, GF is expressed with respect to the modified evolution operator on the complex contour using the two time measurement scheme, the modified evolution operator is expressed in terms of the modified Hamiltonian. Using Keldysh NEGF technique, GF has the form of Fredholm determinant in terms of Greens functions and self-energies in the time domain. In the long time limit, the celebrated Levitov-Lesovik's formula and the fluctuation relation are derived from this formalism. GF of charge statistics for the quantum point contact system in the transient regime is obtained as well. The transient dynamics in lead-dot-lead transport system, including the cumulants of transferred charges and waiting time distribution defined under the transient regime for different temperatures is investigated numerically. A detailed description on how to calculate the GF in the time domain is presented. Generalizations of the formalism to the ferromagnet-normal-ferromagnet system to investigate the FCS of charge current, spin current and spin transfer torque (STT) are presented. GFs in time domain are Fredholm determinants expressed by NEGF as well. As an application of FCS, a formalism using FCS of STT in the long time limit to calculate the switching probability of a nanomagnet system is proposed. The formalism enables us to calculate the switching probability for nonequilibrium systems which are non-Gaussian. From the stochastic Landau-Lifshitz-Gilbert (LLG) equation, the contributions to the change of the anisotropic energy, one is from the power gain due to Gilbert damping and the other is from power dissipation due to the spin transfer torque, were derived. Optimal path approximation which requires the nanomagnet a modestly large volume is presented and the approximation greatly reduces the numerical complexities. This formalism could be used to predict the switching probability numerically for real systems in combination with the first principle calculation.
DegreeDoctor of Philosophy
SubjectTransport theory
Green's functions
Quantum statistics
Dept/ProgramPhysics
Persistent Identifierhttp://hdl.handle.net/10722/233943

 

DC FieldValueLanguage
dc.contributor.authorTang, Gaomin-
dc.contributor.author唐高民-
dc.date.accessioned2016-10-07T01:44:37Z-
dc.date.available2016-10-07T01:44:37Z-
dc.date.issued2016-
dc.identifier.citationTang, G. [唐高民]. (2016). Full-counting statistics of charge and spin transport. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.-
dc.identifier.urihttp://hdl.handle.net/10722/233943-
dc.description.abstractThis thesis investigates the full-counting statistics (FCS) of charge and spin transport using nonequilibrium Green's function (NEGF) in non-interacting systems. Generating function (GF) encodes all the distribution information and is the key of FCS. For the charge statistics, GF is expressed with respect to the modified evolution operator on the complex contour using the two time measurement scheme, the modified evolution operator is expressed in terms of the modified Hamiltonian. Using Keldysh NEGF technique, GF has the form of Fredholm determinant in terms of Greens functions and self-energies in the time domain. In the long time limit, the celebrated Levitov-Lesovik's formula and the fluctuation relation are derived from this formalism. GF of charge statistics for the quantum point contact system in the transient regime is obtained as well. The transient dynamics in lead-dot-lead transport system, including the cumulants of transferred charges and waiting time distribution defined under the transient regime for different temperatures is investigated numerically. A detailed description on how to calculate the GF in the time domain is presented. Generalizations of the formalism to the ferromagnet-normal-ferromagnet system to investigate the FCS of charge current, spin current and spin transfer torque (STT) are presented. GFs in time domain are Fredholm determinants expressed by NEGF as well. As an application of FCS, a formalism using FCS of STT in the long time limit to calculate the switching probability of a nanomagnet system is proposed. The formalism enables us to calculate the switching probability for nonequilibrium systems which are non-Gaussian. From the stochastic Landau-Lifshitz-Gilbert (LLG) equation, the contributions to the change of the anisotropic energy, one is from the power gain due to Gilbert damping and the other is from power dissipation due to the spin transfer torque, were derived. Optimal path approximation which requires the nanomagnet a modestly large volume is presented and the approximation greatly reduces the numerical complexities. This formalism could be used to predict the switching probability numerically for real systems in combination with the first principle calculation.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject.lcshTransport theory-
dc.subject.lcshGreen's functions-
dc.subject.lcshQuantum statistics-
dc.titleFull-counting statistics of charge and spin transport-
dc.typePG_Thesis-
dc.identifier.hkulb5793636-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplinePhysics-
dc.description.naturepublished_or_final_version-

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