Low-Dimensional Systems: Interactions and Transport Properties (Lecture Notes in Physics, 544)

✍ Scribed by Tobias Brandes (editor)

• Publisher: Springer
• Year: 2000
• Tongue: English
• Leaves: 212
• Edition: 2000
• Category: Library

✦ Synopsis

Experimental progress over the past few years has made it possible to test a n- ber of fundamental physical concepts related to the motion of electrons in low dimensions. The production and experimental control of novel structures with typical sizes in the sub-micrometer regime has now become possible. In parti- lar, semiconductors are widely used in order to con?ne the motion of electrons in two-dimensional heterostructures. The quantum Hall e?ect was one of the ?rst highlights of the new physics that is revealed by this con?nement. In a further step of the technological development in semiconductor-heterostructures, other arti?cial devices such as quasi one-dimensional ‘quantum wires’ and ‘quantum dots’ (arti?cial atoms) have also been produced. These structures again di?er very markedly from three- and two-dimensional systems, especially in relation to the transport of electrons and the interaction with light. Although the technol- ical advances and the experimental skills connected with these new structures are progressing extremely fast, our theoretical understanding of the physical e?ects (such as the quantum Hall e?ect) is still at a very rudimentary level. In low-dimensional structures, the interaction of electrons with one another and with other degrees of freedoms such as lattice vibrations or light gives rise to new phenomena that are very di?erent from those familiar in the bulk ma- rial. The theoretical formulation of the electronic transport properties of small devices may be considered well-established, provided interaction processes are neglected.

✦ Table of Contents

Chapter 1
1 Introduction
2 A Critical Review of Theorie of the DC Conductance
2.1 Problems and Limitations of the Kubo Formula when Applied to Mesoscopie Conductors
2.2 Scattering-Theoretical Approaches
3 Combined Use of Microscopic Theory and Thermodynamics [21]
3.1 Conductance of the 1d Fermi Liquid
3.2 Conductance of the Tomonaga–Luttinger Liquid [21]
4 Projection Theory [44,45]
4.1 Decomposition of the 3d Electron Field [44]
4.2 Hamiltonian for the 1d and the Reservoir Fields [44]
4.3 Equation of Motion for the Reduced Density Operator [44,45]
4.4 Current of the 1d Field [44]
4.5 Application of the Projection Theory to the Case where Impurity Scatterings are Present in All Regions [45]
4.6 Application of the Projection Theory to the Case where e-e Scatterings are Present in All Regions [45]
4.7 Advantages of the Projection Theory
5 Appearance of a Non-mechanical Force
6 Deviation from the Quantized Conductance
Acknowledgment
References
Chapter 2
1 Introduction
2 Landauer Type Model
3 Linear Response Theory
4 T ermal Green’s Function Technique
4.1 Thermal Green's Function and Retarded Green's Function
4.2 Calculation of the Green's Function in 1D Channel
5 Calculation of Conductance–Landauer Formula
6 Effects of Electron–Electron Interaction
6.1 Vertex Corrections
6.2 Conductance of 1D Fermi Liquid
6.3 Conductance of Tomonaga–Luttinger Liquid
7 Summary and Discussion
Acknowledgments
References
Chapter 3
1 Introduction
2 Hamiltonia of a Two-Subband Quantum Wire
2.1 Classificatio of Scattering Processes
2.2 Bosonized Form of the Hamiltonian
3 Spinless Electrons
3.1 Nearly Equivalent Subbands
3.2 Non-Equivalent Subbands Renormalization Group
4 Electrons with Spins
5 Conductance
5.1 No Disorder
5.2 Disordered Wire
6 Single-Particle Density of States
6.1 Tunneling Preliminaries
6.2 Warm-Up DOS of a Half-Filled Hubbard Chain
7 Tunneling into the End of a Gapped Wire
8 Experimental Consequencies and Conclusions
Acknowledgements
References
Chapter 4
1 Introduction
2 Semiconductor Wires
2.1 Ballistic Transport
2.2 Power-Law Dependence
3 Modulated Wires
3.1 Born Approximation
3.2 Double Barrier Scattering
3.3 Periodic Potential Scattering
4 Conclusions
References
Chapter 5
1 Introduct on
2 Universal Model of Metallic Nanotubes
2.1 Microscopic Theory
2.2 Bosonization
2.3 Impurity Scattering
3 Luttinger Model Limit
4 Effect of Impurities
5 Effect of Interactions Beyond the Luttinger Model
6 Mott-Insulating Phase
7 Observability of the Mott-Insulating Phase
8 Conclusions
9 Acknowledgments
References
Chapter 6
1 Introduction
2 Pair Excitations of Non-interacting Electrons in One Dimension
3 The Linearized Two-Band Hamiltonian
4 The collective eigenmodes
5 The Raman Cross Section
6 Resonant Intraband Raman Spectra
7 Interband Raman Spectra Approachin Resonance
8 Comparison with Experiments
9 Conclusions
References
Chapter 7
1 Introduction
2 Diagrammatic Language
2.1 Diagrams on the Keldysh Contour
2.2 Superoperator Notation
3 Kinetic Equation
3.1 General Approach
3.2 Exact Solution
4 Renormalization Group
5 Exact Solution of the RG Equations
6 Summary nd Outlook
Acknowledgements
Appendix
References
Chapter 8
Introduction
Spin Blockade in Quantum Dots
Introduction
Magic Numbers
Results and Discussion
Tomonaga-Luttinger System in Magnetic Fiels
Introduction
Formulation
Results and Discussion
Nagative Magnetoresistance Originating from Electron Correlation
Introduction
Formulation
Results and Discussion
Conclusion
References
Chapter 9
1 Introduction
2 Anisotropic Transport Properties
3 Quantum Smectic Model
4 Screening Dependence of Scaling Dimensions
5 Summary
Acknowledgements
References
Chapter 10
1 Introduction
2 Elementary Theorie for the Spin Magnetization
3 A Diagrammatic Approach to the Thermodynamics at v=1
4 Other Theoretical Approaches and Comparison with Experiment
5 Summary
Acknowledgements
References