Efnisyfirlit

• Condensed Matter Physics
• Contents
• Preface
• References
• I ATOMIC STRUCTURE
• 1 The Idea of Crystals
• 1.1 Introduction
• 1.1.1 Why are Solids Crystalline?
• 1.2 Two-Dimensional Lattices
• 1.2.1 Bravais Lattices
• 1.2.2 Enumeration of Two-Dimensional Bravais Lattices
• 1.2.3 Lattices with Bases
• 1.2.4 Primitive Cells
• 1.2.5 Wigner–Seitz Cells
• 1.3 Symmetries
• 1.3.1 The Space Group
• 1.3.2 Translation and Point Groups
• 1.3.3 Role of Symmetry
• Problems
• References
• 2 Three-Dimensional Lattices
• 2.1 Introduction
• 2.2 Monatomic Lattices
• 2.2.1 The Simple Cubic Lattice
• 2.2.2 The Face-Centered Cubic Lattice
• 2.2.3 The Body-Centered Cubic Lattice
• 2.2.4 The Hexagonal Lattice
• 2.2.5 The Hexagonal Close-Packed Lattice
• 2.2.6 The Diamond Lattice
• 2.3 Compounds
• 2.3.1 Rocksalt—Sodium Chloride
• 2.3.2 Cesium Chloride
• 2.3.3 Fluorite—Calcium Fluoride
• 2.3.4 Zincblende—Zinc Sulfide
• 2.3.5 Wurtzite—Zinc Oxide
• 2.3.6 Perovskite—Calcium Titanate
• 2.4 Classification of Lattices by Symmetry
• 2.4.1 Fourteen Bravais Lattices and Seven Crystal Systems
• 2.5 Symmetries of Lattices with Bases
• 2.5.1 Thirty-Two Crystallographic Point Groups
• 2.5.2 Two Hundred Thirty Distinct Lattices
• 2.6 Some Macroscopic Implications of Microscopic Symmetries
• 2.6.1 Pyroelectricity
• 2.6.2 Piezoelectricity
• 2.6.3 Optical Activity
• Problems
• References
• 3 Scattering and Structures
• 3.1 Introduction
• 3.2 Theory of Scattering from Crystals
• 3.2.1 Special Conditions for Scattering
• 3.2.2 Elastic Scattering from Single Atom
• 3.2.3 Wave Scattering from Many Atoms
• 3.2.4 Lattice Sums
• 3.2.5 Reciprocal Lattice
• 3.2.6 Miller Indices
• 3.2.7 Scattering from a Lattice with a Basis
• 3.3 Experimental Methods
• 3.3.1 Laue Method
• 3.3.2 Rotating Crystal Method
• 3.3.3 Powder Method
• 3.4 Further Features of Scattering Experiments
• 3.4.1 Interaction of X-Rays with Matter
• 3.4.2 Production of X-Rays
• 3.4.3 Neutrons
• 3.4.4 Electrons
• 3.4.5 Deciphering Complex Structures
• 3.4.6 Accuracy of Structure Determinations
• 3.5 Correlation Functions
• 3.5.1 Why Bragg Peaks Survive Atomic Motions
• 3.5.2 Extended X-Ray Absorption Fine Structure (EXAFS)
• 3.5.3 Dynamic Light Scattering
• 3.5.4 Application to Dilute Solutions
• Problems
• References
• 4 Surfaces and Interfaces
• 4.1 Introduction
• 4.2 Geometry of Interfaces
• 4.2.1 Coherent and Commensurate Interfaces
• 4.2.2 Stacking Period and Interplanar Spacing
• 4.2.3 Other Topics in Surface Structure
• 4.3 Experimental Observation and Creation of Surfaces
• 4.3.1 Low-Energy Electron Diffraction (LEED)
• 4.3.2 Reflection High-Energy Electron Diffraction (RHEED)
• 4.3.3 Molecular Beam Epitaxy (MBE)
• 4.3.4 Field Ion Microscopy (FIM)
• 4.3.5 Scanning Tunneling Microscopy (STM)
• 4.3.6 Atomic Force Microscopy (AFM)
• 4.3.7 High Resolution Electron Microscopy (HREM)
• Problems
• References
• 5 Beyond Crystals
• 5.1 Introduction
• 5.2 Diffusion and Random Variables
• 5.2.1 Brownian Motion and the Diffusion Equation
• 5.2.2 Diffusion
• 5.2.3 Derivation from Master Equation
• 5.2.4 Connection Between Diffusion and Random Walks
• 5.3 Alloys
• 5.3.1 Equilibrium Structures
• 5.3.2 Phase Diagrams
• 5.3.3 Superlattices
• 5.3.4 Phase Separation
• 5.3.5 Nonequilibrium Structures in Alloys
• 5.3.6 Dynamics of Phase Separation
• 5.4 Simulations
• 5.4.1 Monte Carlo
• 5.4.2 Molecular Dynamics
• 5.5 Liquids
• 5.5.1 Order Parameters and Long-and Short-Range Order
• 5.5.2 Packing Spheres
• 5.6 Glasses
• 5.7 Liquid Crystals
• 5.7.1 Nematics, Cholesterics, and Smectics
• 5.7.2 Liquid Crystal Order Parameter
• 5.8 Polymers
• 5.8.1 Ideal Radius of Gyration
• 5.9 Colloids and Diffusing-Wave Scattering
• 5.9.1 Colloids
• 5.9.2 Diffusing-Wave Spectroscopy
• 5.10 Quasicrystals
• 5.10.1 One-Dimensional Quasicrystal
• 5.10.2 Two-Dimensional Quasicrystals—Penrose Tiles
• 5.10.3 Experimental Observations
• 5.11 Fullerenes and nanotubes
• Problems
• References
• II ELECTRONIC STRUCTURE
• 6 The Free Fermi Gas and Single Electron Model
• 6.1 Introduction
• 6.2 Starting Hamiltonian
• 6.3 Densities of States
• 6.3.1 Definition of Density of States D
• 6.3.2 Results for Free Electrons
• 6.4 Statistical Mechanics of Noninteracting Electrons
• 6.5 Sommerfeld Expansion
• 6.5.1 Specific Heat of Noninteracting Electrons at Low Temperatures
• Problems
• References
• 7 Non–Interacting Electrons in a Periodic Potential
• 7.1 Introduction
• 7.2 Translational Symmetry—Bloch’s Theorem
• 7.2.1 One Dimension
• 7.2.2 Bloch’s Theorem in Three Dimensions
• 7.2.3 Formal Demonstration of Bloch’s Theorem
• 7.2.4 Additional Implications of Bloch’s Theorem
• 7.2.5 Van Hove Singularities
• 7.2.6 Kronig–Penney Model
• 7.3 Rotational Symmetry—Group Representations
• 7.3.1 Classes and Characters
• 7.3.2 Consequences of point group symmetries for Schrödinger’s equation
• Problems
• References
• 8 Nearly Free and Tightly Bound Electrons
• 8.1 Introduction
• 8.2 Nearly Free Electrons
• 8.2.1 Degenerate Perturbation Theory
• 8.3 Brillouin Zones
• 8.3.1 Nearly Free Electron Fermi Surfaces
• 8.4 Tightly Bound Electrons
• 8.4.1 Linear Combinations of Atomic Orbitals
• 8.4.2 Wannier Functions
• 8.4.3 Geometric Phases
• 8.4.4 Tight Binding Model
• Problems
• References
• 9 Electron–Electron Interactions
• 9.1 Introduction
• 9.2 Hartree and Hartree–Fock Equations
• 9.2.1 Variational Principle
• 9.2.2 Hartree–Fock Equations
• 9.2.3 Numerical Implementation
• 9.2.4 Hartree–Fock Equations for Jellium
• 9.3 Density Functional Theory
• 9.3.1 Thomas–Fermi Theory
• 9.3.2 Stability of Matter
• 9.4 Quantum Monte Carlo
• 9.4.1 Integrals by Monte Carlo
• 9.4.2 Quantum Monte Carlo Methods
• 9.4.3 Physical Results
• 9.5 Kohn–Sham Equations
• Problems
• References
• 10 Realistic Calculations in Solids
• 10.1 Introduction
• 10.2 Numerical Methods
• 10.2.1 Pseudopotentials and Orthogonalized Planes Waves (OPW)
• 10.2.2 Linear Combination of Atomic Orbitals (LCAO)
• 10.2.3 Plane Waves
• 10.2.4 Linear Augmented Plane Waves (LAPW)
• 10.3 Definition of Metals, Insulators, and Semiconductors
• 10.4 Brief Survey of the Periodic Table
• 10.4.1 Nearly Free Electron Metals
• 10.4.2 Noble Gases
• 10.4.3 Semiconductors
• 10.4.4 Transition Metals
• 10.4.5 Rare Earths
• Problems
• References
• III MECHANICAL PROPERTIES
• 11 Cohesion of Solids
• 11.1 Introduction
• 11.1.1 Radii of Atoms
• 11.2 Noble Gases
• 11.3 Ionic Crystals
• 11.3.1 Ewald Sums
• 11.4 Metals
• 11.4.1 Use of Pseudopotentials
• 11.5 Band Structure Energy
• 11.5.1 Peierls Distortion
• 11.5.2 Structural Phase Transitions
• 11.6 Hydrogen-Bonded Solids
• 11.7 Cohesive Energy from Band Calculations
• 11.8 Classical Potentials
• Problems
• References
• 12 Elasticity
• 12.1 Introduction
• 12.2 Nonlinear Elasticity
• 12.2.1 Rubber Elasticity
• 12.2.2 Larger Extensions of Rubber
• 12.3 Linear Elasticity
• 12.3.1 Solids of Cubic Symmetry
• 12.3.2 Isotropic Solids
• 12.4 Other Constitutive Laws
• 12.4.1 Liquid Crystals
• 12.4.2 Granular Materials
• Problems
• References
• 13 Phonons
• 13.1 Introduction
• 13.2 Vibrations of a Classical Lattice
• 13.2.1 Classical Vibrations in One Dimension
• 13.2.2 Classical Vibrations in Three Dimensions
• 13.2.3 Normal Modes
• 13.2.4 Lattice with a Basis
• 13.3 Vibrations of a Quantum–Mechanical Lattice
• 13.3.1 Phonon Specific Heat
• 13.3.2 Einstein and Debye Models
• 13.3.3 Thermal Expansion
• 13.4 Inelastic Scattering from Phonons
• 13.4.1 Neutron Scattering
• 13.4.2 Formal Theory of Neutron Scattering
• 13.4.3 Averaging Exponentials
• 13.4.4 Evaluation of Structure Factor
• 13.4.5 Kohn Anomalies
• 13.5 The Mössbauer Effect
• Problems
• References
• 14 Dislocations and Cracks
• 14.1 Introduction
• 14.2 Dislocations
• 14.2.1 Experimental Observations of Dislocations
• 14.2.2 Force to Move a Dislocation
• 14.2.3 One-Dimensional Dislocations: Frenkel–Kontorova Model
• 14.3 Two-Dimensional Dislocations and Hexatic Phases
• 14.3.1 Impossibility of Crystalline Order in Two Dimensions
• 14.3.2 Orientational Order
• 14.3.3 Kosterlitz–Thouless–Berezinskii Transition
• 14.4 Cracks
• 14.4.1 Fracture of a Strip
• 14.4.2 Stresses Around an Elliptical Hole
• 14.4.3 Stress Intensity Factor
• 14.4.4 Atomic Aspects of Fracture
• Problems
• References
• 15 Fluid Mechanics
• 15.1 Introduction
• 15.2 Newtonian Fluids
• 15.2.1 Euler’s Equation
• 15.2.2 Navier–Stokes Equation
• 15.3 Polymeric Solutions
• 15.4 Plasticity
• 15.5 Superfluid 4He
• 15.5.1 Two-Fluid Hydrodynamics
• 15.5.2 Second Sound
• 15.5.3 Direct Observation of Two Fluids
• 15.5.4 Origin of Superfluidity
• 15.5.5 Lagrangian Theory of Wave Function
• 15.5.6 Superfluid 3He
• Problems
• References
• IV ELECTRON TRANSPORT
• 16 Dynamics of Bloch Electrons
• 16.1 Introduction
• 16.1.1 Drude Model
• 16.2 Semiclassical Electron Dynamics
• 16.2.1 Bloch Oscillations
• 16.2.2 K . P Method
• 16.2.3 Effective Mass
• 16.3 Noninteracting Electrons in an Electric Field
• 16.3.1 Zener Tunneling
• 16.4 Semiclassical Equations from Wave Packets
• 16.4.1 Formal Dynamics of Wave Packets
• 16.4.2 Dynamics from Lagrangian
• 16.5 Quantizing Semiclassical Dynamics
• 16.5.1 Wannier–Stark Ladders
• 16.5.2 de Haas–van Alphen Effect
• 16.5.3 Experimental Measurements of Fermi Surfaces
• Problems
• References
• 17 Transport Phenomena and Fermi Liquid Theory
• 17.1 Introduction
• 17.2 Boltzmann Equation
• 17.2.1 Boltzmann Equation
• 17.2.2 Including Anomalous Velocity
• 17.2.3 Relaxation Time Approximation
• 17.2.4 Relation to Rate of Production of Entropy
• 17.3 Transport Symmetries
• 17.3.1 Onsager Relations
• 17.4 Thermoelectric Phenomena
• 17.4.1 Electrical Current
• 17.4.2 Effective Mass and Holes
• 17.4.3 Mixed Thermal and Electrical Gradients
• 17.4.4 Wiedemann–Franz Law
• 17.4.5 Thermopower—Seebeck Effect
• 17.4.6 Peltier Effect
• 17.4.7 Thomson Effect
• 17.4.8 Hall Effect
• 17.4.9 Magnetoresistance
• 17.4.10 Anomalous Hall Effect
• 17.5 Fermi Liquid Theory
• 17.5.1 Basic Ideas
• 17.5.2 Statistical Mechanics of Quasi-Particles
• 17.5.3 Effective Mass
• 17.5.4 Specific Heat
• 17.5.5 Fermi Liquid Parameters
• 17.5.6 Traveling Waves
• 17.5.7 Comparison with Experiment in 3He
• Problems
• References
• 18 Microscopic Theories of Conduction
• 18.1 Introduction
• 18.2 Weak Scattering Theory of Conductivity
• 18.2.1 General Formula for Relaxation Time
• 18.2.2 Matthiessen’s Rule
• 18.2.3 Fluctuations
• 18.3 Metal–Insulator Transitions in Disordered Solids
• 18.3.1 Impurities and Disorder
• 18.3.2 Non-Compensated Impurities and the Mott Transition
• 18.4 Compensated Impurity Scattering and Green’s Functions
• 18.4.1 Tight-Binding Models of Disordered Solids
• 18.4.2 Green’s Functions
• 18.4.3 Single Impurity
• 18.4.4 Coherent Potential Approximation
• 18.5 Localization
• 18.5.1 Exact Results in One Dimension
• 18.5.2 Scaling Theory of Localization
• 18.5.3 Comparison with Experiment
• 18.6 Luttinger Liquids
• 18.6.1 Density of States
• Problems
• References
• 19 Electronics
• 19.1 Introduction
• 19.2 Metal Interfaces
• 19.2.1 Work Functions
• 19.2.2 Schottky Barrier
• 19.2.3 Contact Potentials
• 19.3 Semiconductors
• 19.3.1 Pure Semiconductors
• 19.3.2 Semiconductor in Equilibrium
• 19.3.3 Intrinsic Semiconductor
• 19.3.4 Extrinsic Semiconductor
• 19.4 Diodes and Transistors
• 19.4.1 Surface States
• 19.4.2 Semiconductor Junctions
• 19.4.3 Boltzmann Equation for Semiconductors
• 19.4.4 Detailed Theory of Rectification
• 19.4.5 Transistor
• 19.5 Inversion Layers
• 19.5.1 Heterostructures
• 19.5.2 Quantum Point Contact
• 19.5.3 Quantum Dot
• Problems
• References
• V OPTICAL PROPERTIES
• 20 Phenomenological Theory
• 20.1 Introduction
• 20.2 Maxwell’s Equations
• 20.2.1 Traveling Waves
• 20.2.2 Mechanical Oscillators as Dielectric Function
• 20.3 Kramers–Kronig Relations
• 20.3.1 Application to Optical Experiments
• 20.4 The Kubo–Greenwood Formula
• 20.4.1 Born Approximation
• 20.4.2 Susceptibility
• 20.4.3 Many-Body Green Functions
• Problems
• References
• 21 Optical Properties of Semiconductors
• 21.1 Introduction
• 21.2 Cyclotron Resonance
• 21.2.1 Electron Energy Surfaces
• 21.3 Semiconductor Band Gaps
• 21.3.1 Direct Transitions
• 21.3.2 Indirect Transitions
• 21.4 Excitons
• 21.4.1 Mott–Wannier Excitons
• 21.4.2 Frenkel Excitons
• 21.4.3 Electron–Hole Liquid
• 21.5 Optoelectronics
• 21.5.1 Solar Cells
• 21.5.2 Lasers
• Problems
• References
• 22 Optical Properties of Insulators
• 22.1 Introduction
• 22.2 Polarization
• 22.2.1 Ferroelectrics
• 22.2.2 Berry phase theory of polarization
• 22.2.3 Clausius–Mossotti Relation
• 22.3 Optical Modes in Ionic Crystals
• 22.3.1 Polaritons
• 22.3.2 Polarons
• 22.3.3 Experimental Observations of Polarons
• 22.4 Point Defects and Color Centers
• 22.4.1 Vacancies
• 22.4.2 F Centers
• 22.4.3 Electron Spin Resonance and Electron Nuclear Double Resonance
• 22.4.4 Other Centers
• 22.4.5 Franck–Condon Effect
• 22.4.6 Urbach Tails
• Problems
• References
• 23 Optical Properties of Metals and Inelastic Scattering
• 23.1 Introduction
• 23.1.1 Plasma Frequency
• 23.2 Metals at Low Frequencies
• 23.2.1 Anomalous Skin Effect
• 23.3 Plasmons
• 23.3.1 Experimental Observation of Plasmons
• 23.4 Interband Transitions
• 23.5 Brillouin and Raman Scattering
• 23.5.1 Brillouin Scattering
• 23.5.2 Raman Scattering
• 23.5.3 Inelastic X-Ray Scattering
• 23.6 Photoemission
• 23.6.1 Measurement of Work Functions
• 23.6.2 Angle-Resolved Photoemission
• 23.6.3 Core-Level Photoemission and Charge-Transfer Insulators
• Problems
• References
• VI MAGNETISM
• 24 Classical Theories of Magnetism and Ordering
• 24.1 Introduction
• 24.2 Three Views of Magnetism
• 24.2.1 From Magnetic Moments
• 24.2.2 From Conductivity
• 24.2.3 From a Free Energy
• 24.3 Magnetic Dipole Moments
• 24.3.1 Spontaneous Magnetization of Ferromagnets
• 24.3.2 Ferrimagnets
• 24.3.3 Antiferromagnets
• 24.4 Mean Field Theory and the Ising Model
• 24.4.1 Domains
• 24.4.2 Hysteresis
• 24.5 Other Order–Disorder Transitions
• 24.5.1 Alloy Superlattices
• 24.5.2 Spin Glasses
• 24.6 Critical Phenomena
• 24.6.1 Landau Free Energy
• 24.6.2 Scaling Theory
• Problems
• References
• 25 Magnetism of Ions and Electrons
• 25.1 Introduction
• 25.2 Atomic Magnetism
• 25.2.1 Hund’s Rules
• 25.2.2 Curie’s Law
• 25.3 Magnetism of the Free-Electron Gas
• 25.3.1 Pauli Paramagnetism
• 25.3.2 Landau Diamagnetism
• 25.3.3 Aharonov–Bohm Effect
• 25.4 Tightly Bound Electrons in Magnetic Fields
• 25.5 Quantum Hall Effect
• 25.5.1 Integer Quantum Hall Effect
• 25.5.2 Fractional Quantum Hall Effect
• Problems
• References
• 26 Quantum Mechanics of Interacting Magnetic Moments
• 26.1 Introduction
• 26.2 Origin of Ferromagnetism
• 26.2.1 Heitler-London Calculation
• 26.2.2 Spin Hamiltonian
• 26.3 Heisenberg Model
• 26.3.1 Indirect Exchange and Superexchange
• 26.3.2 Ground State
• 26.3.4 Spin Waves in Antiferromagnets
• 26.3.5 Comparison with Experiment
• 26.4 Ferromagnetism in Transition Metals
• 26.4.1 Stoner Model
• 26.4.2 Calculations Within Band Theory
• 26.5 Spintronics
• 26.5.1 Giant Magnetoresistance
• 26.5.2 Spin Torque
• 26.6 Kondo Effect
• 26.6.1 Scaling Theory
• 26.7 Hubbard Model
• 26.7.1 Mean-Field Solution
• Problems
• References
• 27 Superconductivity
• 27.1 Introduction
• 27.2 Phenomenology of Superconductivity
• 27.2.1 Phenomenological Free Energy
• 27.2.2 Thermodynamics of Superconductors
• 27.2.3 Landau–Ginzburg Free Energy
• 27.2.4 Type I and Type II Superconductors
• 27.2.5 Flux Quantization
• 27.2.6 The Josephson Effect
• 27.2.7 Circuits with Josephson Junction Elements
• 27.2.8 SQUIDS
• 27.2.9 Origin of Josephson’s Equations
• 27.3 Microscopic Theory of Superconductivity
• 27.3.1 Electron–Ion Interaction
• 27.3.2 Instability of the Normal State: Cooper Problem
• 27.3.3 Self-Consistent Ground State
• 27.3.4 Thermodynamics of Superconductors
• 27.3.5 Superconductor in External Magnetic Field
• 27.3.6 Derivation of Meissner Effect
• 27.3.7 Comparison with Experiment
• 27.3.8 High-Temperature Superconductors
• Problems
• References
• APPENDICES
• A Lattice Sums and Fourier Transforms
• A.1 One-Dimensional Sum
• A.2 Area Under Peaks
• A.3 Three-Dimensional Sum
• A.4 Discrete Case
• A.5 Convolution
• A.6 Using the Fast Fourier Transform
• References
• B Variational Techniques
• B.l Functionals and Functional Derivatives
• B.2 Time-Independent Schrödinger Equation
• B.3 Time-Dependent Schrödinger Equation
• B.4 Method of Steepest Descent
• References
• C Second Quantization
• C.l Rules
• C.1.1 States
• C.1.2 Operators
• C.1.3 Hamiltonians
• C.2 Derivations
• C.2.1 Bosons
• C.2.2 Fermions
• Index