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1 Introduction1

1.1 1900-19101

1.2 Crystal Growth2

1.3 Materials by Design4

1.4 Artificial Structures5

2 Crystal Structures9

2.1 Lattice Vectors9

2.2 Reciprocal Lattice Vectors11

2.3 Two Dimensions13

2.4 Three Dimensions15

2.5 Compounds19

2.6 Measuring Crystal Structures21

2.6.1 X-ray Scattering22

2.6.2 Electron Scattering23

2.6.3 Neutron Scattering23

2.7 Structure Factor25

2.8 EXAFS26

2.9 Optical Lattices28

3 Energy Bands31

3.1 Bloch's Theorem31

3.1.1 Floquet's Theorem32

3.2 Nearly Free Electron Bands36

3.2.1 Periodic Potentials36

3.3 Tight-binding Bands38

3.3.1 s-State Bands38

3.3.2 p-State Bands41

3.3.3 Wannier Functions43

3.4 Semiconductor Energy Bands44

3.4.1 What Is a Semiconductor？44

3.4.2 Si，Ge，GaAs47

3.4.3 HgTe and CdTe50

3.4.4 k·p Theory51

3.4.5 Electron Velocity55

3.5 Density of States55

3.5.1 Dynamical Mean Field Theory58

3.6 Pseudopotentials60

3.7 Measurement of Energy Bands62

3.7.1 Cyclotron Resonance62

3.7.2 Synchrotron Band Mapping63

4 Insulators68

4.1 Rare Gas Solids68

4.2 Ionic Crystals69

4.2.1 Madelung energy71

4.2.2 Polarization Interactions72

4.2.3 Van der Waals Interaction75

4.2.4 Ionic Radii75

4.2.5 Repulsive Energy76

4.2.6 Phonons77

4.3 Dielectric Screening78

4.3.1 Dielectric Function78

4.3.2 Polarizabilities80

4.4 Ferroelectrics82

4.4.1 Microscopic Theory83

4.4.2 Thermodynamics87

4.4.3 SrTiO389

4.4.4 BaTiO391

5 Free Electron Metals94

5.1 Introduction94

5.2 Free Electrons96

5.2.1 Electron Density96

5.2.2 Density of States97

5.2.3 Nonzero Temperatures98

5.2.4 Two Dimensions101

5.2.5 Fermi Surfaces102

5.2.6 Thermionic Emission104

5.3 Magnetic Fields105

5.3.1 Integer Quantum Hall Effect107

5.3.2 Fractional Quantum Hall Effect110

5.3.3 Composite Fermions113

5.3.4 deHaas-van Alphen Effect113

5.4 Quantization of Orbits117

5.4.1 Cyclotron Resonance119

6 Electron-Electron Interactions127

6.1 Second Quantization128

6.1.1 Tight-binding Models131

6.1.2 Nearly Free Electrons131

6.1.3 Hartree Energy:Wigner-Seitz134

6.1.4 Exchange Energy136

6.1.5 Compressibility138

6.2 Density Operator141

6.2.1 Two Theorems142

6.2.2 Equations of Morion143

6.2.3 Plasma Oscillations144

6.2.4 Exchange Hole146

6.3 Density Functional Theory148

6.3.1 Functional Denvatives149

6.3.2 Kinetic Energy150

6.3.3 Kohn-Sham Equations151

6.3.4 Exchange and Correlation152

6.3.5 Application to Atoms154

6.3.6 Time-dependent Local Density Approximation155

6.3.7 TDLDA in Solids157

6.4 Dielectric Function158

6.4.1 Random Phase Approximation159

6.4.2 Properties of P（q,ω）161

6.4.3 Hubbard-Singwi Dielectric Functions164

6.5 Impurities in Metals165

6.5.1 Friedel Analysis166

6.5.2 RKKY Interaction170

7 Phonons176

7.1 Phonon Dispersion176

7.1.1 Spring Constants177

7.1.2 Example：Square Lattice179

7.1.3 Polar Crystals181

7.1.4 Phonons181

7.1.5 Dielectric Function185

7.2 Phonon Operators187

7.2.1 Simple Harmonic Oscillator187

7.2.2 Phonons in One Dimension189

7.2.3 Binary Chain192

7.3 Phonon Density of States195

7.3.1 Phonon Heat Capacity197

7.3.2 Isotopes199

7.4 Local Modes203

7.5 Elasticity205

7.5.1 Stress and Strain205

7.5.2 Isotropic Materials208

7.5.3 Boundary Conditions210

7.5.4 Defect Interactions211

7.5.5 Piezoelectricity214

7.5.6 Phonon Focusing215

7.6 Thermal Expansion216

7.7 Debye-Waller Factor217

7.8 Solitons220

7.8.1 Solitary Waves220

7.8.2 Cnoidal Functions222

7.8.3 Periodic Solutions223

8 Boson Systems230

8.1 Second Quantization230

8.2 Superfluidity232

8.2.1 Bose-Einstein Condensation232

8.2.2 Bogoliubov Theory of Superfluidity234

8.2.3 Off-diagonal Long-range Order240

8.3 Spin Waves244

8.3.1 Jordan-Wigner Transformation245

8.3.2 Holstein-Primakoff Transformation247

8.3.3 Heisenberg Model248

9 Electron-Phonon Interactions254

9.1 Semiconductors and Insulators254

9.1.1 Deformation Potentials255

9.1.2 Fr？hlich Interaction257

9.1.3 Piezoelectric Interaction258

9.1.4 Tight-binding Models259

9.1.5 Electron Self-energies260

9.2 Electron-Phonon Interaction in Metals263

9.2.1 λ264

9.2.2 Phonon Frequencies267

9.2.3 Electron-Phonon Mass Enhancement268

9.3 Peierls Transition272

9.4 Phonon-mediated Interactions276

9.4.1 Fixed Electrons276

9.4.2 Dynamical Phonon Exchange278

9.5 Electron-Phonon Efiects at Defects281

9.5.1 F-Centers281

9.5.2 Jahn-Teller Effect284

10 Extrinsic Semiconductors287

10.1 Introduction287

10.1.1 Impurities and Defects in Silicon288

10.1.2 Donors289

10.1.3 Statistical Mechanics of Defects292

10.1.4 n-p Product294

10.1.5 Chemical Potential295

10.1.6 Schottky Barriers297

10.2 Localization301

10.2.1 Mott Localization301

10.2.2 Anderson Localization304

10.2.3 Weak Localization304

10.2.4 Percolation306

10.3 Variable Range Hopping310

10.4 Mobility Edge311

10.5 Band Gap Narrowing312

11 Transport Phenomena320

11.1 Introduction320

11.2 Drude Theory321

11.3 Bloch Oscillations322

11.4 Boltzmann Equation324

11.5 Currents327

11.5.1 Transport Coeffcients327

11.5.2 Metals329

11.5.3 Semiconductors and Insulators333

11.6 Impurity Scattering335

11.6.1 Screened Impurity Scattering336

11.6.2 T-matrix Description337

11.6.3 Mooij Correlation338

11.7 Electron-Phonon Interaction340

11.7.1 Lifetime341

11.7.2 Semiconductors343

11.7.3 Saturation Velocity344

11.7.4 Metals347

11.7.5 Temperature Relaxation348

11.8 Ballistic Transport350

11.9 Carrier Drag353

11.10 Electron Tunneling355

11.10.1 Giaever Tunneling356

11.10.2 Esaki Diode358

11.10.3 Schottky Barrier Tunneling361

11.10.4 Efiective Mass Matching362

11.11 Phonon Transport364

11.11.1 Transport in Three Dimensions364

11.11.2 Minimum Thermal Conductivity365

11.11.3 Kapitza Resistance366

11.11.4 Measuring Thermal Conductivity368

11.12 Thermoelectric Devices370

11.12.1 Maximum Cooling371

11.12.2 Refrigerator373

11.12.3 Power Generation374

12 Optical Properties379

12.1 Introduction379

12.1.1 Optical Functions379

12.1.2 Kramers-Kronig Analysis381

12.2 Simple Metals383

12.2.1 Drude383

12.3 Force-Force Correlations385

12.3.1 Impurity Scattering386

12.3.2 Interband Scattering388

12.4 Optical Absorption389

12.4.1 Interband Transitions in Insulators389

12.4.2 Wannier Excitons392

12.4.3 Frenkel Excitons395

12.5 X-Ray Edge Singularity396

12.6 Photoemission399

12.7 Conducting Polymers401

12.8 Polaritons404

12.8.1 Phonon Polaritons404

12.8.2 Plasmon Polaritons405

12.9 Surface Polaritons406

12.9.1 Surface Plasmons408

12.9.2 Surface Optical Phonons410

12.9.3 Surface Charge Density413

13 Magnetism418

13.1 Introduction418

13.2 Simple Magnets418

13.2.1 Atomic Magnets418

13.2.2 Hund's Rules418

13.2.3 Curie's Law420

13.2.4 Ferromagnetism422

13.2.5 Antiferromagnetism423

13.3 3d Metals424

13.4 Theories of Magnetism425

13.4.1 Ising and Heisenberg Models425

13.4.2 Mean Field Theory427

13.4.3 Landau Theory431

13.4.4 Critical Phenomena433

13.5 Magnetic Susceptibility434

13.6 Ising Model436

13.6.1 One Dimension436

13.6.2 Two and three Dimensions437

13.6.3 Bethe Lattice439

13.6.4 Order-Disorder Transitions443

13.6.5 Lattice Gas445

13.7 Topological Phase Transitions446

13.7.1 Vortices447

13.7.2 XY-Model448

13.8 Kondo Effect452

13.8.1 sd-Interaction453

13.8.2 Spin-flip Scattering454

13.8.3 Kondo Resonance456

13.9 Hubbard Model458

13.9.1 U＝0 Solution459

13.9.2 Atomic Limit460

13.9.3 U＞0460

13.9.4 Half-filling462

14 Superconductivity467

14.1 Discovery of Superconductivity467

14.1.1 Zero resistance467

14.1.2 Meissner Effect468

14.1.3 Three Eras of Superconductivity469

14.2 Theories of Superconductivity473

14.2.1 London Equation473

14.2.2 Ginzburg-Landau Theory475

14.2.3 Type Ⅱ478

14.3 BCS Theory479

14.3.1 History of Theory479

14.3.2 Effective Hamiltonian480

14.3.3 Pairing States481

14.3.4 Gap Equation483

14.3.5 d-Wave Energy Gaps486

14.3.6 Density of States487

14.3.7 Ultrasonic Attenuation489

14.3.8 Meissner Effect490

14.4 ElectTon Tunneling492

14.4.1 Normal-Superconductor494

14.4.2 Superconductor-Superconductor497

14.4.3 Josephson Tunneling498

14.4.4 Andreev Tunneling501

14.4.5 Corner Junctions502

14.5 Cuprate Superconductors503

14.5.1 Muon Rotation503

14.5.2 Magnetic Oscillations506

14.6 Flux Quantization507

15 Nanometer Physics511

15.1 Quantum Wells512

15.1.1 Lattice Matching512

15.1.2 Electron States513

15.1.3 Excitons and Donors in Quantum Wells515

15.1.4 Modulation Doping518

15.1.5 Electron Mobility520

15.2 Graphene520

15.2.1 Structure521

15.2.2 Electron Energy Bands522

15.2.3 Eigenvectors525

15.2.4 Landau Levels525

15.2.5 Electron-Phonon Interaction526

15.2.6 Phonons528

15.3 Carbon Nanotubes530

15.3.1 Chirality530

15.3.2 Electronic States531

15.3.3 Phonons in Carbon Nanotubes536

15.3.4 Electrical Resistivity537

Appendix541

Index553