Contents Preface Physical Constants, Units, Mathematical Signs and Symbols Introduction Kinetic Theory and the Boltzmann Equation

Transcription

1 V Contents Preface XI Physical Constants, Units, Mathematical Signs and Symbols 1 Introduction Carbon Nanotubes Theoretical Background Metals and Conduction Electrons Quantum Mechanics Heisenberg Uncertainty Principle Bosons and Fermions Fermi and Bose Distribution Functions Composite Particles Quasifree Electron Model Electrons and Holes The Gate Field Effect Book Layout Suggestions for Readers Second Quantization Semiclassical Theory of Electron Dynamics Fermi Surface 9 References 10 2 Kinetic Theory and the Boltzmann Equation Diffusion and Thermal Conduction Collision Rate: Mean Free Path Electrical Conductivity and Matthiessen s Rule The Hall Effect: Electrons and Holes The Boltzmann Equation The Current Relaxation Rate 21 References 25 3 Bloch Electron Dynamics Bloch Theorem in One Dimension The Kronig Penney Model 30 XV

2 VI Contents 3.3 Bloch Theorem in Three Dimensions Fermi Liquid Model The Fermi Surface Heat Capacity and Density of States The Density of State in the Momentum Space Equations of Motion for a Bloch Electron 46 References 51 4 Phonons and Electron Phonon Interaction Phonons and Lattice Dynamics Van Hove Singularities Particles on a Stretched String (Coupled Harmonic Oscillators) Low-Frequency Phonons Discussion Electron Phonon Interaction Phonon-Exchange Attraction 71 References 75 5 Electrical Conductivity of Multiwalled Nanotubes Introduction Graphene Lattice Stability and Reflection Symmetry Single-Wall Nanotubes Multiwalled Nanotubes Summary and Discussion 87 References 89 6 Semiconducting SWNTs Introduction Single-Wall Nanotubes Summary and Discussion 98 References 98 7 Superconductivity Basic Properties of a Superconductor Zero Resistance Meissner Effect Ring Supercurrent and Flux Quantization Josephson Effects Energy Gap Sharp Phase Change Occurrence of a Superconductor Elemental Superconductors Compound Superconductors High-T c Superconductors Theoretical Survey The Cause of Superconductivity 107

3 Contents VII The Bardeen Cooper Schrieffer Theory Quantum Statistical Theory Quantum Statistical Theory of Superconductivity The Generalized BCS Hamiltonian The Cooper Pair Problem Moving Pairons The BCS Ground State The Reduced Generalized BCS Hamiltonian The Ground State Remarks The Nature of the Reduced Hamiltonian Binding Energy per Pairon The Energy Gap The Energy Gap Equation Neutral Supercondensate Cooper Pairs (Pairons) Formation of a Supercondensate and Occurrence of Superconductors Blurred Fermi Surface Bose Einstein Condensation in 2D Discussion 137 References Metallic (or Superconducting) SWNTs Introduction Graphene The Full Hamiltonian Moving Pairons The Bose Einstein Condensation of Pairons Superconductivity in Metallic SWNTs High-Field Transport in Metallic SWNTs Zero-Bias Anomaly Temperature Behavior and Current Saturation Summary 162 References Magnetic Susceptibility Magnetogyric Ratio Pauli Paramagnetism The Landau States and Levels Landau Diamagnetism 171 References Magnetic Oscillations Onsager s Formula Statistical Mechanical Calculations: 3D 181

4 VIII Contents 10.3 Statistical Mechanical Calculations: 2D Anisotropic Magnetoresistance in Copper Introduction Theory Discussion Shubnikov de Haas Oscillations 196 References Quantum Hall Effect Experimental Facts Theoretical Developments Theory of the Quantum Hall Effect Introduction The Model The Integer QHE The Fractional QHE Discussion 218 References Quantum Hall Effect in Graphene Introduction 221 References Seebeck Coefficient in Multiwalled Carbon Nanotubes Introduction Classical Theory of the Seebeck Coefficient in a Metal Quantum Theory of the Seebeck Coefficient in a Metal Simple Applications Graphene and Carbon Nanotubes Conduction in Multiwalled Carbon Nanotubes Seebeck Coefficient in Multiwalled Carbon Nanotubes 243 References Miscellaneous Metal Insulator Transition in Vanadium Dioxide Introduction Conduction Electrons in Graphite Coronet Fermi Surface in Beryllium Magnetic Oscillations in Bismuth 251 References 251 Appendix 253 A.1 Second Quantization 253 A.1.1 Boson Creation and Annihilation Operators 253 A.1.2 Observables 256 A.1.3 Fermion Creation and Annihilation Operators 257 A.1.4 Heisenberg Equation of Motion 259

5 Contents IX A.2 Eigenvalue Problem and Equation-of-Motion Method 261 A.2.1 Energy-Eigenvalue Problem in Second Quantization 261 A.2.2 Energies of Quasielectrons (or Electrons ) at 0 K 264 A.3 Derivation of the Cooper Equation (7.34) 267 A.4 Proof of (7.94) 270 A.5 Statistical Weight for the Landau States 271 A.5.1 The Three-Dimensional Case 271 A.5.2 The Two-Dimensional Case 272 A.6 Derivation of Formulas (11.16) (11.18) 273 References 274 Index 275

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