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

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