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研究生: 涂維元
Tu, Wei-Yuan
論文名稱: 介觀量子輸運及量子干涉元件中的電子同調動力學
Dynamics of Electron Coherence in Mesoscopic Quantum Transport and Interference Devices
指導教授: 張為民
Zhang, Wei-Min
學位類別: 博士
Doctor
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 142
中文關鍵詞: AB干涉儀量子同調性電子動力學
外文關鍵詞: AB interferometer, quantum coherence, electron dynamics
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  • 在此論文中我們探討在量子輸運及量子干涉系統中的電子同調性。我們特別關注雙量子點Aharonov-Bohm干涉儀在這方面的物理特性。這個簡單的系統提供了一個整合的平台,讓我們可以在一個統一的框架下探索在許多量子輸運系統中都普遍出現的各式議題,包括量子同調性,量子耗散和干涉。藉由對於該系統的精確主方程求解,我們研究了雙量子電所有電子組態的動態變化;我們也調查了該干涉儀的暫態輸運行為。除此之外,我們也更進一步將自旋以及自旋軌道角動量耦合考慮進同樣的體系,並且研究了該系統自旋相關的動態輸運特性。綜合上述研究結果,我們將對量子輸運與干涉元件中的電子同調性提出我們的觀點。

    In this thesis, we investigate electron coherence in quantum transport and interference devices. In particular, we specifically focus on the physical properties of a double-quantum-dot Aharonov-Bohm interferometer. This simple system is an ideal platform for exploring the issues of quantum coherence, dissipation and interference that prevail in many quantum transport systems in a unified framework. By solving an exact master equation, we study explicitly the dynamics of the full electronic configurations of the double-quantum-dot system. We also investigate the transient transport dynamics of such interferometer. We further make an extension to include spin-orbit interaction in the same setup and examine the time-dependent spin-resolved transport dynamics. By comprehending the properties of various physical quantities, we provide a perspective on electron coherence in quantum transport and interference devices.

    Abstract i Abstract in Chinese ii Acknowledgement iii Contents vi List of Figures xi 1 Introduction 1 1.1 General motivations, the scope and the outline of the thesis .1 1.2 Perspectives on electron coherence ......3 1.2.1 Electronic analogs of optics .......3 1.2.2 Addressing electron quantum states in nanoelectronic systems 6 2 Quantum-dot Aharonov-Bohm interferometers 11 2.1 The AB effect in mesoscopic transport .....11 2.2 Transmission phase and Single-QD AB interferometer ...12 2.3 Coherent mode and DQD AB interferometers .....14 3 Theories for transport through nanostructures 17 3.1 Formal description of the problem ......17 3.1.1 Physical quantities to be monitored .....18 3.2 Time-dependent transport theories .......20 3.3 Landauer-B¨utikker formalism ........21 3.3.1 Scattering matrix ........22 3.3.2 From scattering matrix to currents .....24 3.4 Schwinger-Keldysh nonequilibrium Green function technique ..........25 3.4.1 Defining Green functions .......27 3.4.2 Transport currents in terms of Green functions ...28 3.4.3 Kadanoff-Baym equations .......29 3.5 Master equation formalism ........31 3.5.1 Exact equation of motion for the reduced density matrix and real-time currents ........32 3.5.2 The general solution for the reduced density matrix ..35 3.5.3 Dissipation-fluctuation dynamical processes and nonequi- librium Green functions .......36 3.6 A comparison ...........38 4 Dynamics of Electron Coherence in DQD AB interferometers 40 4.1 Preliminary formulae .........41 4.1.1 Results in the wide-band limit ......43 4.2 Decoherence dynamics ........44 4.2.1 Phase localization .........45 4.2.2 Effects of nondegeneracy and asymmetric couplings on the intrinsic coherence ........47 4.2.3 Summary .........49 4.3 Coherent control of molecular states by the magnetic flux ...50 4.3.1 Real-time processes of molecular-state formations ...52 4.3.2 Periodicity in flux .........52 4.3.3 Summary .........53 5 Interference dynamics and flux-dependent transient quantum transport 62 5.1 Analytical expressions for the occupation numbers and the currents ......62 5.2 Coherence and phase rigidity at steady state ....66 5.3 Real-time dynamics ........68 5.3.1 Degenerate DQD with asymmetric couplings to the leads (δE = 0, δΓ 6= 0) .........68 5.3.2 Non-degenerate DQD with symmetric coupling to the leads (δE 6= 0, δΓ = 0) .........69 5.3.3 Non-degenerate DQD with asymmetric coupling to the leads (δE 6= 0, δΓ 6= 0) .........70 5.4 Summary ...........71 6 Extension to spin-resolved coherent transport through DQD AB interferometers with spin-orbit interaction 77 6.1 Background and motivation .......77 6.2 Nonequilibrium formalism with spins ......80 6.3 Real-time transport through a DQD AB interferometer with SOI .83 6.3.1 The model ..........83 6.3.2 Formalisms for real-time spin-dependent currents ...84 6.4 Spin-dependent current in the steady state ....90 6.5 Dynamics of spin-resolved transport . ...92 6.5.1 Time developments of full spin polarization in transport current ...........92 6.5.2 Dynamics of spin currents ......95 6.6 Summary ...........99 7 Conclusion and potential extensive topics 106 A Transmission through a DQD AB interferometer 111 A.1 Tight-binding construction of the device Hamiltonian ...111 A.2 Transmission amplitude from solving the Schr¨odinger equation ..112 B Derivation of Eq.(3.40) 114 B.1 Fermion coherent state representation of the reduced density matrix114 B.2 The Fock state representation of the reduced density matrix at arbitrary time ...........115 C Stationary limit of Eq.(4.22) 116 D Gauge independence 117 D.1 The formal solutions of the Green functions for arbitrary spectral densities ............117 D.2 The dependence of the density matrix on the phases φL and φR .119 D.3 The phase dependence of contribution from individual level to the current ...........119 E Small and large bias limits of the steady state at zero temperature 120 F Determination of SOI induced phase and the characteristic directions from the bonding geometry and SOI strength 123 G The current formulae for a single level coupled to one and two electron reservoirs 125 G.1 The current through a spinless single level coupled to one lead ..125 G.2 The current through a spinless single level coupled to two leads .126 Bibliography 126

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