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CHAPTER 1 Basic Properties of Crystals1

1.1 Crystal Lattices2

1.1.1 Primitive Cell3

1.1.2 UnitCell3

1.1.3 Wigner-SeitzCell3

1.1.4 Lattice Point Group3

1.2 Bravais Lattices in Two and Three Dimensions4

1.2.1 Simple Cubic (sc)Lattice4

1.2.2 Lattice Constants5

1.2.3 Coordination Numbers5

1.2.4 Body-Centered Cubic(bcc)Lattice5

1.2.5 Face-Centered Cubic(fcc)Lattice7

1.2.6 Other Bravais Lattices9

1.3 Lattice Planes and Miller Indices11

1.4 Bravais Lattices and Crystal Structures13

1.4.1 Crystal Structure13

1.4.2 Lattice with a Basis13

1.4.3 Packing Fraction14

1.5 Crystal Derects and Surface Effects14

1.5.1 Crystal Defects14

1.5.2 Surface Effects14

1.6 Some Simple Crystal Structures15

1.6.1 Sodium Chloride Structure15

1.6.2 Cesium Chloride Structure15

1.6.3 Diamond Structure16

1.6.4 Zincblende Structure17

1.6.5 Hexagonal Close-Packed(hcp)Structure17

1.7 Bragg Diffraction19

1.8 Laue Method20

1.9 Reciprocal Lattice21

1.9.1 Definition21

1.9.2 Properties of the Reciprocal Lattice22

1.9.3 Alternative Formulation of the Laue Condition25

1.10 Brillouin Zones27

1.10.1 Definition27

1.10.2 One-Dimensional Lattice28

1.10.3 Two-Dimensional Square Lattice28

1.10.4 bcc Lattice29

1.10 5 fcc Lattice30

1.11 Diffraction by a Crystal Lattice with a Basis31

1.11.1 Theory31

1.11.2 Geornetrical Structure Factor32

1.11.3 Application to bcc Lattice32

1.11.4 Application to fcc Lattice33

1.11.5 The Atomic Scattering Factor or Form Factor33

Problems34

References35

CHAPTER 2 Phonons and Lattice Vibrations37

2.1 Lattice Dynamics37

2.1.1 Theorv37

2.1.2 Normal Modes of a One-Dimensional Monoatomic Lattice41

2.1.3 Normal Modes of a One-Dimensional Chain with a Basis44

2.2 Lattice Specific Heat48

2.2.1 Theory48

2.2.2 The Debye Model of Specific Heat49

2.2.3 The Einstein Model of Specific Heat52

2.3 Second Quantization53

2.3.1 Occupation Number Representation53

2.3.2 Creation and Annihilation Operators54

2.3.3 Field Operators and the Hamiltonian58

2.4 Quantization of Lattice Waves61

2.4.1 Formulation61

2.4.2 Quantization of Lattice Waves65

Problems66

References68

CHAPTER 3 Free Electron Model71

3.1 The Classical(Drude)Model of a Metal71

3.2 Sommerfeld Model73

3.2.1 Introduction73

3.2.2 Fermi Distribution Function74

3.2.3 Density Operator75

3.2.4 Free Electron Fermi Gas77

3.2.5 Ground-State Energy of the Electron Gas79

3.2.6 Density of Electron States81

3.3 Fermi Energy and the Chemical Potential82

3.4 Specific Heat of the Electron Gas84

3.5 DC Electrical Conductivity86

3.6 The Hall Effect87

3.7 Failures of the Free Electron Model89

Problems90

References93

CHAPTER 4 Nearly Free Electron Model95

4.1 Electrons in a Weak Periodic Potential96

4.1.1 Introduction96

4.1.2 Plane Wave Solutions97

4.2 Bloch Functions and Bloch Theorem99

4.3 Reduced,Repeated(Periodic),and Extended Zone Schemes99

4.3.1 Reduced Zone Scheme100

4.3.2 Repeated Zone Scheme100

4.3.3 Extended Zone Scheme101

4.4 Band Index101

4.5 Effective Hamiltonian102

4.6 Proof of Bloch's Theorem from Translational Symmetry103

4.7 Approximate Solution Near a Zone Boundary105

4.8 Different Zone Schemes109

4.8.1 Reduced Zone Scheme109

4.8.2 Extended Zone Scheme110

4.8.3 Periodic Zone Scheme111

4.9 Elementary Band Theory of Solids111

4.9.1 Introduction111

4.9.2 Energy Bands in One Dimension112

4.9.3 Number of States in a Band112

4.10 Metals,Insulators,and Semiconductors112

4.11 Brillouin Zones117

4.12 Fermi Surface119

4.12.1 Fermi Surface (in Two Dimensions)119

4.12.2 Fermi Surface (in Three Dimensions)121

4.12.3 Harrison's Method of Construction of the Fermi Surface121

Problems124

References130

CHAPTER 5 Band-Structure Calculations131

5.1 Introduction131

5.2 Tight-Binding Approximation131

5.3 LCAO Method135

5.4 Wannier Functions140

5.5 Cellular Method142

5.6 Orthogonalized Plane-Wave(OPW)Method145

5.7 Pseudopotentials147

5.8 Muffin-Tin Potential149

5.9 Augmented Plane-Wave(APW)Method150

5.10 Green's Function (KKR)Method152

5.11 Model Pseudopotentials156

5.12 Empirical Pseudopotentials157

5.13 First-Principles Pseudopotentials158

Problems160

References163

CHAPTER 6 Static and Transport Properties of Solids165

6.1 Band Picture166

6.2 Bond Picture167

6.3 Diamond Structure168

6.4 Si and Ge168

6.5 Zinc-Blende Semiconductors170

6.6 Ionic Solids172

6.7 Molecular Crystals174

6.7.1 Molecular Solids174

6.7.2 Hydrogen-Bonded Structures174

6.8 Cohesion of Solids174

6.8.1 Molecular Crystals:Noble Gases174

6.8.2 Ionic Crystals176

6.8.3 Covalent Crystals177

6.8.4 Cohesion in Metals178

6.9 The Semiclassical Model179

6.10 Liouville's Theorem182

6.11 Boltzmann Equation183

6.12 Relaxation Time Approximation184

6.13 Electrical Conductivity186

6.14 Thermal Conductivity187

6.15 Weak Scattering Theory of Conductivity188

6.15.1 Relaxation Time and Scattering Probability188

6.15.2 The Collision Term188

6.15.3 Impurity Scattering189

6.16 Resistivity Due to Scattering by Phonons192

Problems194

References196

CHAPTER 7 Electron-Electron Interaction199

7.1 Introduction199

7.2 Hartree Approximation200

7.3 Hartree-Fock Approximation203

7.3.1 General Formulation203

7.3.2 Hartree-Fock Theory for Jellium204

7.4 Effect of Screening207

7.4.1 General Formulation207

7.4.2 Thomas-Fermi Approximation208

7.4.3 Lindhard Theory of Screening209

7.5 Friedel Sum Rule and Oscillations214

7.6 Frequency and Wave-Number-Dependent Dielectric Constant217

7.7 Mott Transition222

7.8 Density Functional Theory223

7.8.1 General Formulation223

7.8.2 Local Density Approximation224

7.9 Fermi Liquid Theory225

7.9.1 Quasiparticles225

7.9.2 Energy Functional227

7.9.3 Fermi Liquid Parameters230

7.10 Green's Function Method232

7.10.1 General Formulation232

7.10.2 Finite-Temperature Green's Function Formalism for Interacting Bloch Electrons233

7.10.3 Exchange Self-Energy in the Band Model234

Problems235

References241

CHAPTER 8 Dynamics of Bloch Electrons243

8.1 Semiclassical Model243

8.2 Velocity Operator244

8.3 k.P Perturbation Theory245

8.4 Quasiclassical Dynamics246

8.5 Effective Mass247

8.6 Bloch Electrons in External Fields248

8.6.1 Time Evolution of Bloch Electrons in an Electric Field250

8.6.2 Alternate Derivation for Bloch Functions in an External Electric and Magnetic Field252

8.6.3 Motion in an Applied DC Field253

8.7 Bloch Oscillations254

8.8 Holes255

8.9 Zener Breakdown(Approximate Method)258

8.10 Rigorous Calculation of Zener Tunneling261

8.11 Electron-Phonon Interaction264

Problems271

References274

CHAPTER 9 Semiconductors275

9.1 Introduction275

9.2 Electrons and Holes278

9.3 Electron and Hole Densities in Equilibrium279

9.4 Intrinsic Semiconductors283

9.5 Extrinsic Semiconductors284

9.6 Doped Semiconductors285

9.7 Statistics of Impurity Levels in Thermal Equilibrium288

9.7.1 Donor Levels288

9.7.2 Acceptor Levels288

9.7.3 Doped Semiconductors289

9.8 Diluted Magnetic Semiconductors290

9.8.1 Introduction290

9.8.2 Magnetization in Zero External Magnetic Field in DMS291

9.8.3 Electron Paramagnetic Resonance Shift291

9.8.4 ？.？Model295

9.9 Zinc Oxide296

9.10 Amorphous Semiconductors296

9.10.1 Introduction296

9.10.2 Linear Combination of Hybrids Model for Tetrahedral Semiconductors297

Problems300

References303

CHAPTER 10 Electronics305

10.1 Introduction305

10.2 p-n Junction306

10.2.1 Introduction306

10.2.2 p-n Junction in Equilibrium307

10.3 Rectification by a p-n Junction311

10.3.1 Equilibrium Case311

10.3.2 Nonequilibrium Case(V≠0)313

10.4 Transistors318

10.4.1 Bipolar Transistors318

10.4.2 Field-Effect Transistor319

10.4.3 Single-Electron Transistor321

10.5 Integrated Circuits325

10.6 Optoelectronic Devices325

10.7 Graphene329

10.8 Graphene-Based Electronics332

Problems333

References336

CHAPTER 11 Spintronics339

11.1 Introduction339

11.2 Magnetoresistance340

11.3 Giant Magnetoresistance340

11.3.1 Metallic Multilayers340

11.4 Mott's Theory of Spin-Dependent Scattering of Electrons342

11.5 Camley-Barnas Model345

11.6 CPP-GMR348

11.6.1 Introduction348

11.6.2 Theory of CPP-GMR of Multilayered Nanowires350

11.7 MTJ,TMR,and MRAM352

11.8 Spin Transfer Torques and Magnetic Switching356

11.9 Spintronics with Semiconductors357

11.9.1 Introduction357

11.9.2 Theory of an FM-T-N Junction358

11.9.3 Injection Coefficient361

Problems364

References367

CHAPTER 12 Diamagnetism and Paramagnetism369

12.1 Introduction370

12.2 Atomic(or Ionic)Magnetic Susceptibilities371

12.2.1 General Formulation371

12.2.2 Larmor Diamagnetism372

12.2.3 Hund's Rules373

12.2.4 Van Vleck Paramagnetism374

12.2.5 Landé g Factor375

12.2.6 Curie's Law377

12.3 Magnetic Susceptibility of Free Electrons in Metals378

12.3.1 General Formulation378

12.3.2 Landau Diamagnetism and Pauli Paramagnetism380

12.3.3 De Haas-van Alphen Effect383

12.4 Many-Body Theory of Magnetic Susceptibility of Bloch Electrons in Solids388

12.4.1 Introduction388

12.4.2 Equation of Motion in the Bloch Representation388

12.4.3 Thermodynamic Potential390

12.4.4 General Formula for X390

12.4.5 Exchange Self-Energy in the Band Model393

12.4.6 Exchange Enhancement of Xs394

12.4.7 Exchange and Correlation Effects on Xo395

12.4.8 Exchange and Correlation Effects on Xso396

12.5 Quantum Hall Effect396

12.5.1 Introduction396

12.5.2 Two-Dimensional Electron Gas396

12.5.3 Quantum Transport of a Two-Dimensional Electron Gas in a Strong Magnetic Field397

12.5.4 Quantum Hall Effect from Gauge Invariance400

12.6 Fractional Quantum Hall Effect400

Problems401

References407

CHAPTER 13 Magnetic Ordering409

13.1 Introduction410

13.2 Magnetic Dipole Moments411

13.3 Models for Ferromagnetism and Antiferromagnetism412

13.3.1 Introduction412

13.3.2 Heitler-London Approximation412

13.3.3 Spin Hamiltonian414

13.3.4 Heisenberg Model416

13.3.5 Direct,Indirect,and Superexchange416

13.3.6 Spin Waves in Ferromagnets:Magnons417

13.3.7 Schwinger Representation417

13.3.8 Application to the Heisenberg Hamiltonian418

13.3.9 Spin Waves in Antiferromagnets421

13.4 Ferromagnetism in Solids422

13.4.1 Ferromagnetism Near the Curie Temperature422

13.4.2 Comparison of Spin-Wave Theory with the Weiss Field Model424

13.4.3 Ferromagnetic Domains425

13.4.4 Hysteresis426

13.4.5 Ising Model427

13.5 Ferromagnetism in Transition Metals427

13.5.1 Introduction427

13.5.2 Stoner Model428

13.5.3 Ferromagnetism in Fe,Co,and Ni from Stoner's Model and Kohn-Sham Equations430

13.5.4 Free Electron Gas Model431

13.5.5 Hubbard Model433

13.6 Magnetization of Interacting Bloch Electrons434

13.6.1 Introduction434

13.6.2 Theory of Magnetization434

13.6.3 The Quasiparticle Contribution to Magnetization435

13.6.4 Contribution of Correlations to Magnetization436

13.6.5 Single-Particle Spectrum and the Criteria for Ferromagnetic Ground State437

13.7 The Kondo Effect439

13.8 Anderson Model439

13.9 The Magnetic Phase Transition440

13.9.1 Introduction440

13.9.2 The Order Parameter441

13.9.3 Landau Theory of Second-Order Phase Transitions441

Problems443

References448

CHAPTER 14 Superconductivity451

14.1 Properties of Superconductors452

14.1.1 Introduction452

14.1.2 Type Ⅰ and Type Ⅱ Superconductors453

14.1.3 Second-Order Phase Transition454

14.1.4 Isotope Effect454

14.1.5 Phase Diagram454

14.2 Meissner-Ochsenfeld Effect455

14.3 The London Equation455

14.4 Ginzburg-Landau Theory456

14.4.1 Order Parameter456

14.4.2 Boundary Conditions457

14.4.3 Coherence Length457

14.4.4 London Penetration Depth458

14.5 Flux Quantization459

14.6 Josephson Effect460

14.6.1 Two Superconductors Separated by an Oxide Layer460

14.6.2 AC and DC Josephson Effects462

14.7 Microscopic Theory of Superconductivity462

14.7.1 Introduction462

14.7.2 Quasi-Electrons463

14.7.3 Cooper Pairs464

14.7.4 BCS Theory466

14.7.5 Ground State of the Superconducting Electron Gas466

14.7.6 Excited States at T=0469

14.7.7 Excited States at T≠0470

14.8 Strong-Coupling Theory472

14.8.1 Introduction472

14.8.2 Upper Limit of the Critical Temperature,Tc472

14.9 High-Temperature Superconductors473

14.9.1 Introduction473

14.9.2 Properties of Novel Superconductors(Cuprates)474

14.9.3 Brief Review of s-,P-,and d-wave Pairing474

14.9.4 Experimental Confirmation of d-wave Pairing476

14.9.5 Search for a Theoretical Mechanism of High Tc Superconductors481

Problems481

References485

CHAPTER 15 Heavy Fermions487

15.1 Introduction488

15.2 Kondo-Lattice,Mixed-Valence,and Heavy Fermions490

15.2.1 Periodic Anderson and Kondo-Lattice Models490

15.2.2 Mixed-Valence Compounds492

15.2.3 Slave Boson Method493

15.2.4 Cluster Calculations494

15.3 Mean-Field Theories498

15.3.1 The Local Impurity Self-Consistent Approximation498

15.3.2 Application of LISA to Periodic Anderson Model499

15.3.3 RKKY Interaction500

15.3.4 Extended Dynamical Mean-field Theory501

15.4 Fermi-Liquid Models502

15.4.1 Heavy Fermi Liquids502

15.4.2 Fractionalized Fermi Liquids505

15.5 Metamagnetism in Heavy Fermions506

15.6 Ce-and U-Based Superconducting Compounds508

15.6.1 Ce-Based Compounds508

15.6.2 U-Based Superconducting Compounds509

15.7 Other Heavy-Fermion Superconductors513

15.7.1 PrOs4Sb12513

15.7.2 PuCoGa5513

15.7.3 PuRhGa5515

15.7.4 Comparison between Cu and Pu Containing High-Tc Superconductors516

15.8 Theories of Heavy-Fermion Superconductivity516

15.9 Kondo Insulators516

15.9.1 Brief Review516

15.9.2 Theory of Kondo Insulators517

Problems519

References524

CHAPTER 16 Metallic Nanoclusters527

16.1 Introduction528

16.1.1 Nanoscience and Nanoclusters528

16.1.2 Liquid Drop Model528

16.1.3 Size and Surface/Volume Ratio528

16.1.4 Geometric and Electronic Shell Structures530

16.2 Electronic Shell Structure531

16.2 1 Spherical Jellium Model(Phenomenological)531

16.2.2 Self-Consistent Spherical Jellium Model532

16.2.3 Ellipsoidal Shell Model535

16.2.4 Nonalkali Clusters535

16.2.5 Large Clusters535

16.3 Geometric Shell Structure537

16.3.1 Close-Packing537

16.3.2 Wulff Construction537

16.3 3 Polyhedra538

16.3.4 Filling between Complete Shells540

16.4 Cluster Growth on Surfaces540

16.4.1 Monte Carlo Simulations540

16.4.2 Mean-Field Rate Equations541

16.5 Structure of Isolated Clusters542

16.5.1 Theoretical Models542

16 5.2 Structure of Some Isolated Clusters546

16.6 Magnetism in Clusters547

16.6.1 Magnetism in Isolated Clusters547

16.6.2 Experimental Techniques for Studying Cluster Magnetism549

16.6.3 Magnetism in Embedded Clusters553

16.6.4 Graphite Surfaces555

16.6.5 Study of Clusters by Scanning Tunneling Microscope555

16.6.6 Clusters Embedded in a Matrix557

16.7 Superconducting State of Nanoclusters558

16.7.1 Qualitative Analysis558

16 7.2 Thermodynamic Green's Function Formalism for Nanoclusters559

Problems562

References565

CHAPTER 17 Complex Structures567

17.1 Liquids568

17.1.1 Introduction568

17.1.2 Phase Diagram568

17.1.3 Van Hove Pair Correlation Function569

17.1.4 Correlation Function for Liquids570

17.2 Superfluid 4He570

17.2.1 Introduction570

17.2.2 Phase Transition in 4He570

17.2.3 Two-Fluid Model for Liquid 4He571

17.2.4 Theory of Superfluidity in Liquid 4He571

17.3 Liquid 3He573

17.3.1 Introduction573

17.3.2 Possibility of Superfluidity in Liquid 3He574

17.3.3 Fermi Liquid Theory574

17.3.4 Experimental Results of Superfluidity in Liquid 3He575

17.3.5 Theoretical Model for the A and A1 Phases575

17.3.6 Theoretical Model for the B Phase577

17.4 Liquid Crystals578

17.4.1 Introduction578

17.4.2 Three Classes of Liquid Crystals578

17.4.3 The Order Parameter580

17.4.4 Curvature Strains581

17.4.5 Optical Properties of Cholesteric Liquid Crystals581

17.5 Quasicrystals583

17.5.1 Introduction583

17.5.2 Penrose Tiles583

17.5.3 Discovery of Quasicrystals584

17.5.4 Quasiperiodic Lattice584

17.5 5 Phonon and Phason Degrees of Freedom586

17.5.6 Dislocation in the Penrose Lattice589

17.5.7 Icosahedral Quasicrystals589

17.6 Amorphous Solids590

17.6.1 Introduction590

17.6.2 Energy Bands in One-Dimensional Aperiodic Potentials591

17.6.3 Density of States593

17.6.4 Amorphous Semiconductors593

Problems594

References597

CHAPTER 18 Novel Materials599

18.1 Graphene600

18.1.1 Introduction600

18.1.2 Graphene Lattice601

18.1.3 Tight-Binding Approximation602

18.1.4 Dirac Fermions606

18.1.5 Comprehensive View of Graphene608

18.2 Fullerenes608

18.2.1 Introduction608

18.2.2 Discovery of C60609

18.3 Fullerenes and Tubules613

18.3.1 Introduction613

18.3.2 Carbon Nauotubeles614

18.3.3 Three Types of Carbon Nanotubes614

18.3.4 Symmetry Properties of Carbon Nanotubes616

18.3.5 Band Structure of a Fullercne Nanotube617

18.4 Polymers617

18.4.1 Introduction617

18.4.2 Saturated and Conjugated Polymers618

18.4.3 Transparent Metallic Polymers621

18.4.4 Electronic Polymers621

18.5 Solitons in Conducting Polymers622

18 5.1 Introduction622

18.5 2 Electronic Structure623

18.5.3 Tight-Binding Model623

18.5.4 Soliton Excitations624

18.5.5 Solitons,Polarons,and Polaron Excitations626

18.6.6 Polarons and Bipolarons626

18.6 Photoinduced Electron Transfer627

Problems627

References630

APPENDIX A Elements of Group Theory633

A.1 Symmetry and Its Consequences633

A.1.1 Symmetry of Crystals633

A.1.2 Definition of a Group633

A.1.3 Symmetry Operations in Crystal Lattices634

A.2 Space Groups634

A.2.1 Introduction634

A.2.2 Space Group Operations634

A.3 Point Group Operations636

A.3.1 Introduction636

A.3.2 Description of Point Groups636

A.3.3 The Cubic Group Oh638

APPENDIX B Mossbauer Effect641

B.1 Introduction641

B.2 Recoilless Fraction642

B.3 Average Transferred Energy643

Reference644

APPENDIX C Introduction to Renormalization Group Approach645

C.1 Critical Behavior645

C.2 Theory for Scaling646

C.3 Renormalization Group Approach648

References649

lndex651