1 Introduction

1.1 1900-1910

1.2 Crystal Growth

1.3 Materials by Design

1.4 Artificial Structures

2 Crystal Structures

2.1 Lattice Vectors

2.2 Reciprocal Lattice Vectors

2.3 Two Dimensions

2.4 Three Dimensions

2.5 Compounds

2.6 Measuring Crystal Structures

2.6.1 X-ray Scattering

2.6.2 Electron Scattering

2.6.3 Neutron Scattering

2.7 Structure Factor

2.8 EXAFS

2.9 Optical Lattices

3 Energy Bands

3.1 Bloch's Theorem

3.1.1 Floquet's Theorem

3.2 Nearly Free Electron Bands

3.2.1 Periodic Potentials

3.3 Tight-binding Bands

3.3.1 s-State Bands

3.3.2 p-State Bands

3.3.3 Wannier Functions

3.4 Semiconductor Energy Bands

3.4.1 What Is a Semiconductor？

3.4.2 Si，Ge，GaAs

3.4.3 HgTe and CdTe

3.4.4 k·p Theory

3.4.5 Electron Velocity

3.5 Density of States

3.5.1 Dynamical Mean Field Theory

3.6 Pseudopotentials

3.7 Measurement of Energy Bands

3.7.1 Cyclotron Resonance

3.7.2 Synchrotron Band Mapping

4 Insulators

4.1 Rare Gas Solids

4.2 Ionic Crystals

4.2.1 Madelung energy

4.2.2 Polarization Interactions

4.2.3 Van der Waals Interaction

4.2.4 Ionic Radii

4.2.5 Repulsive Energy

4.2.6 Phonons

4.3 Dielectric Screening

4.3.1 Dielectric Function

4.3.2 Polarizabilities

4.4 Ferroelectrics

4.4.1 Microscopic Theory

4.4.2 Thermodynamics

4.4.3 SrTiO3

4.4.4 BaTiO3

5 Free Electron Metals

5.1 Introduction

5.2 Free Electrons

5.2.1 Electron Density

5.2.2 Density of States

5.2.3 Nonzero Temperatures

5.2.4 Two Dimensions

5.2.5 Fermi Surfaces

5.2.6 Thermionic Emission

5.3 Magnetic Fields

5.3.1 Integer Quantum Hall Effect

5.3.2 Fractional Quantum Hall Effect

5.3.3 Composite Fermions

5.3.4 deHaas-van Alphen Effect

5.4 Quantization of Orbits

5.4.1 Cyclotron Resonance

6 Electron-Electron Interactions

6.1 Second Quantization

6.1.1 Tight-binding Models

6.1.2 Nearly Free Electrons

6.1.3 Hartree Energy:Wigner-Seitz

6.1.4 Exchange Energy

6.1.5 Compressibility

6.2 Density Operator

6.2.1 Two Theorems

6.2.2 Equations of Morion

6.2.3 Plasma Oscillations

6.2.4 Exchange Hole

6.3 Density Functional Theory

6.3.1 Functional Denvatives

6.3.2 Kinetic Energy

6.3.3 Kohn-Sham Equations

6.3.4 Exchange and Correlation

6.3.5 Application to Atoms

6.3.6 Time-dependent Local Density Approximation

6.3.7 TDLDA in Solids

6.4 Dielectric Function

6.4.1 Random Phase Approximation

6.4.2 Properties of P（q,ω）

6.4.3 Hubbard-Singwi Dielectric Functions

6.5 Impurities in Metals

6.5.1 Friedel Analysis

6.5.2 RKKY Interaction

7 Phonons

7.1 Phonon Dispersion

7.1.1 Spring Constants

7.1.2 Example：Square Lattice

7.1.3 Polar Crystals

7.1.4 Phonons

7.1.5 Dielectric Function

7.2 Phonon Operators

7.2.1 Simple Harmonic Oscillator

7.2.2 Phonons in One Dimension

7.2.3 Binary Chain

7.3 Phonon Density of States

7.3.1 Phonon Heat Capacity

7.3.2 Isotopes

7.4 Local Modes

7.5 Elasticity

7.5.1 Stress and Strain

7.5.2 Isotropic Materials

7.5.3 Boundary Conditions

7.5.4 Defect Interactions

7.5.5 Piezoelectricity

7.5.6 Phonon Focusing

7.6 Thermal Expansion

7.7 Debye-Waller Factor

7.8 Solitons

7.8.1 Solitary Waves

7.8.2 Cnoidal Functions

7.8.3 Periodic Solutions

8 Boson Systems

8.1 Second Quantization

8.2 Superfluidity

8.2.1 Bose-Einstein Condensation

8.2.2 Bogoliubov Theory of Superfluidity

8.2.3 Off-diagonal Long-range Order

8.3 Spin Waves

8.3.1 Jordan-Wigner Transformation

8.3.2 Holstein-Primakoff Transformation

8.3.3 Heisenberg Model

9 Electron-Phonon Interactions

9.1 Semiconductors and Insulators

9.1.1 Deformation Potentials

9.1.2 Fr？hlich Interaction

9.1.3 Piezoelectric Interaction

9.1.4 Tight-binding Models

9.1.5 Electron Self-energies

9.2 Electron-Phonon Interaction in Metals

9.2.1 λ

9.2.2 Phonon Frequencies

9.2.3 Electron-Phonon Mass Enhancement

9.3 Peierls Transition

9.4 Phonon-mediated Interactions

9.4.1 Fixed Electrons

9.4.2 Dynamical Phonon Exchange

9.5 Electron-Phonon Efiects at Defects

9.5.1 F-Centers

9.5.2 Jahn-Teller Effect

10 Extrinsic Semiconductors

10.1 Introduction

10.1.1 Impurities and Defects in Silicon

10.1.2 Donors

10.1.3 Statistical Mechanics of Defects

10.1.4 n-p Product

10.1.5 Chemical Potential

10.1.6 Schottky Barriers

10.2 Localization

10.2.1 Mott Localization

10.2.2 Anderson Localization

10.2.3 Weak Localization

10.2.4 Percolation

10.3 Variable Range Hopping

10.4 Mobility Edge

10.5 Band Gap Narrowing

11 Transport Phenomena

11.1 Introduction

11.2 Drude Theory

11.3 Bloch Oscillations

11.4 Boltzmann Equation

11.5 Currents

11.5.1 Transport Coeffcients

11.5.2 Metals

11.5.3 Semiconductors and Insulators

11.6 Impurity Scattering

11.6.1 Screened Impurity Scattering

11.6.2 T-matrix Description

11.6.3 Mooij Correlation

11.7 Electron-Phonon Interaction

11.7.1 Lifetime

11.7.2 Semiconductors

11.7.3 Saturation Velocity

11.7.4 Metals

11.7.5 Temperature Relaxation

11.8 Ballistic Transport

11.9 Carrier Drag

11.10 Electron Tunneling

11.10.1 Giaever Tunneling

11.10.2 Esaki Diode

11.10.3 Schottky Barrier Tunneling

11.10.4 Efiective Mass Matching

11.11 Phonon Transport

11.11.1 Transport in Three Dimensions

11.11.2 Minimum Thermal Conductivity

11.11.3 Kapitza Resistance

11.11.4 Measuring Thermal Conductivity

11.12 Thermoelectric Devices

11.12.1 Maximum Cooling

11.12.2 Refrigerator

11.12.3 Power Generation

12 Optical Properties

12.1 Introduction

12.1.1 Optical Functions

12.1.2 Kramers-Kronig Analysis

12.2 Simple Metals

12.2.1 Drude

12.3 Force-Force Correlations

12.3.1 Impurity Scattering

12.3.2 Interband Scattering

12.4 Optical Absorption

12.4.1 Interband Transitions in Insulators

12.4.2 Wannier Excitons

12.4.3 Frenkel Excitons

12.5 X-Ray Edge Singularity

12.6 Photoemission

12.7 Conducting Polymers

12.8 Polaritons

12.8.1 Phonon Polaritons

12.8.2 Plasmon Polaritons

12.9 Surface Polaritons

12.9.1 Surface Plasmons

12.9.2 Surface Optical Phonons

12.9.3 Surface Charge Density

13 Magnetism

13.1 Introduction

13.2 Simple Magnets

13.2.1 Atomic Magnets

13.2.2 Hund's Rules

13.2.3 Curie's Law

13.2.4 Ferromagnetism

13.2.5 Antiferromagnetism

13.3 3d Metals

13.4 Theories of Magnetism

13.4.1 Ising and Heisenberg Models

13.4.2 Mean Field Theory

13.4.3 Landau Theory

13.4.4 Critical Phenomena

13.5 Magnetic Susceptibility

13.6 Ising Model

13.6.1 One Dimension

13.6.2 Two and three Dimensions

13.6.3 Bethe Lattice

13.6.4 Order-Disorder Transitions

13.6.5 Lattice Gas

13.7 Topological Phase Transitions

13.7.1 Vortices

13.7.2 XY-Model

13.8 Kondo Effect

13.8.1 sd-Interaction

13.8.2 Spin-flip Scattering

13.8.3 Kondo Resonance

13.9 Hubbard Model

13.9.1 U＝0 Solution

13.9.2 Atomic Limit

13.9.3 U＞0

13.9.4 Half-filling

14 Superconductivity

14.1 Discovery of Superconductivity

14.1.1 Zero resistance

14.1.2 Meissner Effect

14.1.3 Three Eras of Superconductivity

14.2 Theories of Superconductivity

14.2.1 London Equation

14.2.2 Ginzburg-Landau Theory

14.2.3 Type Ⅱ

14.3 BCS Theory

14.3.1 History of Theory

14.3.2 Effective Hamiltonian

14.3.3 Pairing States

14.3.4 Gap Equation

14.3.5 d-Wave Energy Gaps

14.3.6 Density of States

14.3.7 Ultrasonic Attenuation

14.3.8 Meissner Effect

14.4 ElectTon Tunneling

14.4.1 Normal-Superconductor

14.4.2 Superconductor-Superconductor

14.4.3 Josephson Tunneling

14.4.4 Andreev Tunneling

14.4.5 Corner Junctions

14.5 Cuprate Superconductors

14.5.1 Muon Rotation

14.5.2 Magnetic Oscillations

14.6 Flux Quantization

15 Nanometer Physics

15.1 Quantum Wells

15.1.1 Lattice Matching

15.1.2 Electron States

15.1.3 Excitons and Donors in Quantum Wells

15.1.4 Modulation Doping

15.1.5 Electron Mobility

15.2 Graphene

15.2.1 Structure

15.2.2 Electron Energy Bands

15.2.3 Eigenvectors

15.2.4 Landau Levels

15.2.5 Electron-Phonon Interaction

15.2.6 Phonons

15.3 Carbon Nanotubes

15.3.1 Chirality

15.3.2 Electronic States

15.3.3 Phonons in Carbon Nanotubes

15.3.4 Electrical Resistivity

Appendix

Index