Electrical Conduction in Graphene and Nanotubes
In: New York Academy of Sciences Series
Electrical Conduction in Graphene and Nanotubes -- Contents -- Preface -- Physical Constants, Units, Mathematical Signs and Symbols -- 1 Introduction -- 1.1 Carbon Nanotubes -- 1.2 Theoretical Background -- 1.2.1 Metals and Conduction Electrons -- 1.2.2 Quantum Mechanics -- 1.2.3 Heisenberg Uncertainty Principle -- 1.2.4 Bosons and Fermions -- 1.2.5 Fermi and Bose Distribution Functions -- 1.2.6 Composite Particles -- 1.2.7 Quasifree Electron Model -- 1.2.8 "Electrons" and "Holes" -- 1.2.9 The Gate Field Effect -- 1.3 Book Layout -- 1.4 Suggestions for Readers -- 1.4.1 Second Quantization -- 1.4.2 Semiclassical Theory of Electron Dynamics -- 1.4.3 Fermi Surface -- References -- 2 Kinetic Theory and the Boltzmann Equation -- 2.1 Diffusion and Thermal Conduction -- 2.2 Collision Rate: Mean Free Path -- 2.3 Electrical Conductivity and Matthiessen's Rule -- 2.4 The Hall Effect: "Electrons" and "Holes" -- 2.5 The Boltzmann Equation -- 2.6 The Current Relaxation Rate -- References -- 3 Bloch Electron Dynamics -- 3.1 Bloch Theorem in One Dimension -- 3.2 The Kronig-Penney Model -- 3.3 Bloch Theorem in Three Dimensions -- 3.4 Fermi Liquid Model -- 3.5 The Fermi Surface -- 3.6 Heat Capacity and Density of States -- 3.7 The Density of State in the Momentum Space -- 3.8 Equations of Motion for a Bloch Electron -- References -- 4 Phonons and Electron-Phonon Interaction -- 4.1 Phonons and Lattice Dynamics -- 4.2 Van Hove Singularities -- 4.2.1 Particles on a Stretched String (Coupled Harmonic Oscillators) -- 4.2.2 Low-Frequency Phonons -- 4.2.3 Discussion -- 4.3 Electron-Phonon Interaction -- 4.4 Phonon-Exchange Attraction -- References -- 5 Electrical Conductivity of Multiwalled Nanotubes -- 5.1 Introduction -- 5.2 Graphene -- 5.3 Lattice Stability and Reflection Symmetry -- 5.4 Single-Wall Nanotubes -- 5.5 Multiwalled Nanotubes -- 5.6 Summary and Discussion.