固体物理学 英文影印版PDF电子书下载

Part Ⅰ An Overview 3

1 Basic Principles Summarized 3

1.1 The Atomic Idea:From Elementary Particles to Solids 4

1.2 Permanent(i.e.,Equilibrium)Structures of Matter Correspond to the Minimum of Their(Free)Energy 6

1.3 Condensed Matter Tends to Collapse Under the Influence of Coulomb Potential Energy 9

1.4 Quantum Kinetic Energy Counterbalances Coulomb Potential Energy Leading to Stable Equilibrium Structures 10

1.4.1 Heisenberg's Uncertainty Principle and the Minimum Kinetic Energy 10

1.4.2 Pauli's Exclusion Principle and the Enhancement of the Minimum Kinetic Energy 11

1.4.3 Schr？dinger's Spectral Discreteness and the Rigidity of the Ground State 14

1.5 Dimensional Analysis 15

1.6 Key Points 18

1.7 Questions and Problems 19

2 Basic Principles in Action 21

2.1 Size and Energy Scale of Atoms 21

2.2 Why do Atoms Come Together to Form Molecules and Solids? 23

2.3 Ionic Motion:Small Oscillations 27

2.4 Why do the Specific Heats of Solids go to Zero as T→0K? 29

2.5 When is Classical Mechanics Adequate? 31

2.6 Estimating Magnitudes Through Dimensional Analysis 32

2.6.1 Atomic Radius,Rα 32

2.6.2 Volume per Atom,νa≡V/Na,in Solids 32

2.6.3 Mass Density,ρM 33

2.6.4 Cohesive Energy,Uc 33

2.6.5 Bulk Modulus,B,and Shear Modulus,μs 34

2.6.6 Sound Velocities in Solids,c0,cl,ct 35

2.6.7 Maximum Angular Frequency of Atomic Vibrations in Solids,ωmax 37

2.6.8 Melting Temperature,Tm 37

2.6.9 DC Electrical Resistivity,ρe 38

2.7 Key Points 41

2.8 Questions and Problems 42

3 A First Acquaintance with Condensed Matter 47

3.1 Various Kinds of Condensed Matter 47

3.1.1 Monocrystalline and Polycrystalline Atomic Solids 48

3.1.2 Atomic or Ionic Compounds and Alloys 49

3.1.3 Molecular Solids 49

3.1.4 Glasses 49

3.1.5 Polymers 50

3.1.6 Colloids 50

3.1.7 Gels 51

3.1.8 Liquid Crystals 51

3.1.9 Self-Assembled Soft Matter 51

3.1.1 0Artificial Structures 52

3.1.1 1Clusters and Other Finite Systems 52

3.2 Bonding Types and Resulting Properties 53

3.2.1 Simple Metals 54

3.2.2 Transition Metals and Rare Earths 55

3.2.3 Covalent Solids 55

3.2.4 Ionic Solids 56

3.2.5 Van der Waals Bonded Solids 57

3.2.6 Hydrogen Bonded Solids 58

3.3 A Short Introduction to Crystal Structures 59

3.3.1 Some Basic Definitions 59

3.3.2 Unit and Primitive Cells of Some Commonly Occurring 3-D Crystal Structures 64

3.3.3 Systems and Types of 3D Bravais Lattices 67

3.3.4 Crystal Planes and Miller Indices 67

3.4 Bloch Theorem,Reciprocal Lattice,Bragg Planes,and Brillouin Zones 70

3.4.1 Bloch Theorem 70

3.4.2 Reciprocal Lattice 72

3.4.3 Bragg Planes 75

3.4.4 Brillouin Zones 75

3.5 Key Points 77

3.6 Questions and Problems 78

Part Ⅱ Two Simple Models for Solids 83

4 The Jellium Model and Metals Ⅰ:Equilibrium Properties 83

4.1 Introduction 84

4.2 Electronic Eigenfunctions,Eigenenergies,Number of States 86

4.3 Kinetic and Potential Energy,Pressures,and Elastic Moduli 90

4.4 Acoustic Waves are the Ionic Eigenoscillations in the JM 97

4.5 Thermodynamic Quantities 101

4.5.1 General Formulas 101

4.5.2 Specific Heat,CV 104

4.5.3 Bulk Thermal Expansion Coefficient 107

4.6 Key Points 107

4.7 Problems 108

5 The Jellium Model and Metals Ⅱ:Response to External Perturbations 113

5.1 Response to Electric Field 113

5.2 The Dielectric Function 114

5.3 Static Electrical Conductivity 120

5.4 Phonon Contribution to Resistivity 123

5.5 Response in the Presence of a Static Uniform Magnetic Field 127

5.5.1 Magnetic Resonances 128

5.5.2 Hall Effect and Magnetoresistance 131

5.5.3 Magnetic Susceptibility,χm 133

5.6 Thermoelectric Response 140

5.7 Key Points 143

5.8 Problems 145

6 Solids as Supergiant Molecules:LCAO 149

6.1 Diversion:The Coupled Pendulums Model 149

6.2 Introductory Remarks Regarding the LCAO Method 152

6.3 A Single Band One-Dimensional Elemental“Metal” 153

6.4 One-Dimensional Ionic“Solid” 157

6.5 One-Dimensional Molecular“Solid” 160

6.6 Diversion:Eigenoscillations in One-Dimensional“solid”with two Atoms Per Primitive Cell 163

6.7 One-Dimensional Elemental sp1“Semiconductor” 164

6.8 One-Dimensional Compound sp1“Semiconductor” 171

6.9 Key Points 174

6.1 0Problems 174

7 Semiconductors and Other Tetravalent Solids 177

7.1 Lattice Structures:A Reminder 177

7.2 Band Edges and Gap 178

7.3 Differences Between the l-D and the 3-D Case and Energy Diagrams 181

7.4 Metals,Semiconductors,and Ionic Insulators 183

7.5 Holes 184

7.6 Effective Masses and DOS 186

7.7 Dielectric Function and Optical Absorption 188

7.8 Effective Hamiltonian 189

7.9 Impurity Levels 191

7.9.1 Impurity Levels:The General Picture 191

7.9.2 Impurity Levels:Doping 192

7.10 Concentration of Electrons and Holes at Temperature T 195

7.10.1 Intrinsic case 197

7.10.2 Extrinsic case 197

7.11 Band Structure and Electronic DOS 198

7.12 Eigenfrequencies,Phononic DOS,and Dielectric Function 200

7.13 Key Points 207

7.14 Problems 208

8 Beyond the Jellium and the LCAO:An Outline 211

8.1 Introductory Remarks 211

8.2 The Four Basic Approximations 212

8.3 Density Functional Theory 215

8.4 Outline of an Advanced Scheme for Calculating the Properties of Solids 219

8.5 Beyond the Four Basic Approximations 221

8.5.1 Periodicity Broken or Absent 223

8.5.2 Electron-Electron Correlations,Quasi-Particles,Magnetic Phases,and Superconductivity 235

8.5.3 Electron-Phonon Interactions,Transport Properties,Superconductivity,and Polarons 237

8.5.4 Phonon-Phonon Interactions,Thermal Expansion,Melting,Structural Phase Transitions,Solitons,Breathers 238

8.5.5 Disorder and Many Body Effects in Coexistence 239

8.5.6 Quantum Informatics and Solid State Systems 240

8.6 Key Points 240

8.7 Problems 241

Part Ⅲ More About Periodicity＆its Consequences 245

9 Crystal Structure and Ionic Vibrations 245

9.1 Experimental Determination of Crystal Structures 245

9.2 Determination of the Frequency vs.Wavevector 251

9.3 Theoretical Calculation of the Phonon Dispersion Relation 256

9.4 The Debye-Waller Factor and the Inelastic Cross-Section 263

9.5 Key Points 268

9.6 Problems 269

10 Electrons in Periodic Media.The Role of Magnetic Field 273

10.1 Introduction 273

10.2 Dispersion Relations,Surfaces of Constant Energy,and DOS:A Reminder 274

10.3 Effective Hamiltonian and Semiclassical Approximation 276

10.4 Semiclassical Trajectories in the Presence of a Magnetic Field 280

10.5 Two Simple but Elucidating TB Models 281

10.6 Cyclotron Resonance and the de Haas-van Alphen Effect 287

10.7 Hall Effect and Magnetoresistance 290

10.8 Key Points 298

10.9 Problems 299

11 Methods for Calculating the Band Structure 301

11.1 Introductory Remarks 301

11.2 Ionic and Total Pseudopotentials 303

11.3 Schr？dinger Equation,Plane Wave Expansion,and Bloch's Theorem 309

11.4 Plane Waves and Perturbation Theory 310

11.5 Muffin-Tin Potential 313

11.6 Schr？dinger Equation and the Augmented Plane Wave(APW)Method 313

11.7 Schr？dinger Equation and the Korringa-Kohn-Rostoker(KKR) Method 315

11.8 The κ·p Method of Band Structure Calculations 317

11.9 Key Points 321

11.1 0Problems 322

12 Pseudopotentials in Action 325

12.1 The One-Dimensional Case 325

12.2 The Two-Dimensional Square Lattice 327

12.2.1 Spaghetti Diagrams 327

12.2.2 Fermi Lines 330

12.3 Harrison's Construction 336

12.4 Second-Order Correction to the Total JM Energy 337

12.5 Ionic Interactions in Real Space 338

12.6 Phononic Dispersions in Metals 340

12.7 Scattering by Phonons,Mean Free Path,and the Dimensionless Constant λ in Metals 342

12.8 Key Points 345

12.9 Problems 346

Part Ⅳ Materials 351

13 Simple Metals and Semiconductors Revisited 351

13.1 Band Structure and Fermi Surfaces of Simple Metals 351

13.1.1 Alkali Metals 351

13.1.2 Alkaline Earths:Be,Mg,Ca,Sr,Ba,and Ra 354

13.1.3 Trivalent Metals 354

13.1.4 Tetravalent Metals 358

13.2 Band Structure of Semiconductors 360

13.3 The Jones Zone and the Disappearance of the Fermi Surface 363

13.4 Mechanical Properties of Semiconductors 365

13.5 Magnetic Susceptibility of Semiconductors 368

13.6 Optical and Transport Properties of Semiconductors 371

13.6.1 Excitons 371

13.6.2 Conductivity and Mobility in Semiconductors 374

13.7 Silicon Dioxide(SiO2) 378

13.8 Graphite and Graphene 380

13.9 Organic semiconductors 386

13.10 Key Points 388

13.11 Questions and Problems 389

14 Closed-Shell Solids 393

14.1 Van Der Waals Solids 393

14.2 Ionic Compounds Ⅰ:Types and Crystal Structures 397

14.3 Ionic Compounds Ⅱ:Mechanical Properties 399

14.4 Ionic Compounds Ⅲ:Optical Properties 401

14.5 Key Points 406

14.6 Problems 407

15 Transition Metals and Compounds 409

15.1 Experimental Data for the Transition Metals 409

15.2 Calculations Ⅰ:APW or KKR 412

15.3 Calculations Ⅱ:LCAO 417

15.4 Calculations Ⅲ:The Simple Friedel Model 421

15.5 Compounds of Transition Elements,Ⅰ:Perovskites 423

15.6 Compounds of Transition Elements,Ⅱ:High Tc Superconducting Materials 426

15.7 Compounds of Transition Metals,Ⅲ:Oxides,etc 430

15.8 Key Points 434

15.9 Problems 435

16 Artificial Periodic Structures 437

16.1 Semiconductor Superlattices 437

16.2 Photonic Crystals:An Overview 439

16.3 Photonic Crystals:Theoretical Considerations 443

16.4 Phononic Crystals 450

16.5 Left-Handed Metamaterials(LHMs) 456

16.6 Designing,Fabricating,and Measuring LHMs 461

16.7 Key Points 466

16.8 Problems 468

Part Ⅴ Deviations from Periodicity 471

17 Surfaces and Interfaces 471

17.1 Surface Preparation 471

17.2 Relaxation and Reconstruction 472

17.3 Surface States 474

17.4 Work Function 479

17.5 Measuring the Work Function 481

17.6 The p-n Homojunction in Equilibrium 483

17.7 The p-n Homojunction Under an External Voltage V 487

17.8 Some Applications of Interfaces 491

17.9 Key Points 494

17.10 Problems 497

18 Disordered and Other Nonperiodic Solids 499

18.1 Introductory Remarks 499

18.2 Alloys and the Hume-Rothery Rule 500

18.3 Glasses and other Amorphous Systems 502

18.4 Distribution and Correlation Functions 504

18.5 Quasi-Crystals 506

18.6 Electron Transport and Quantum Interference 510

18.7 Band Structure,Static Disorder,and Localization 513

18.7.1 3D Case 513

18.7.2 2D Case 517

18.7.3 1D and quasi 1D Systems 518

18.8 Calculation Techniques 522

18.8.1 Coherent Potential Approximation 522

18.8.2 Weak Localization due to Quantum Interference 526

18.8.3 Scaling Approach 529

18.8.4 Quasi-One-Dimensional Systems and Scaling 532

18.8.5 Potential Well Analogy 533

18.9 Quantum Hall Effect 534

18.10 Key Points 538

18.11 Problems 540

19 Finite Systems 543

19.1 Introduction 543

19.2 Metallic Clusters 544

19.3 Fullerenes 545

19.4 C60-Based Solids 549

19.5 Carbon Nanotubes 551

19.6 Other Clusters 556

19.7 Quantum Dots 557

19.7.1 An Overview 557

19.7.2 Optical Transitions 558

19.7.3 QDs and Coulomb Blockade 561

19.8 Key Points 564

19.9 Problems 565

Part Ⅵ Correlated Systems 569

20 Magnetic Materials,Ⅰ:Phenomenology 569

20.1 Which Property Characterizes These Materials? 569

20.2 Experimental Data for Ferromagnets 573

20.2.1 Saturation Magnetization vs Temperature for Simple Ferromagnets 573

20.2.2 Magnetic Susceptibility of Simple Ferromagnet for T>Tc 573

20.2.3 Saturation Magnetization vs Temperature for Ferrimagnets 574

20.2.4 Magnetic Susceptibility of Ferrimagnets vs Temperature(T>Tc) 575

20.3 Experimental Data for Antiferromagnets 576

20.3.1 Determination of the Antiferromagnetic Ordered Structure 576

20.3.2 Magnetic Susceptibility vs Temperature 577

20.4 Materials 577

20.4.1 Simple Ferromagnetic Materials 577

20.4.2 Ferrimagnetic Materials 579

20.4.3 Antiferromagnetic Materials 580

20.5 Thermodynamic Relations 580

20.5.1 Thermodynamic Potentials 580

20.5.2 Mean Field Approximation(Landau's Approach) 583

20.5.3 Why are Magnetic Domains Formed? 584

20.5.4 How Thick is the Bloch Wall? 586

20.5.5 Examples of Magnetic Domains 586

20.5.6 Thermodynamics of Antiferromagnets 587

20.6 Spintronics 588

20.7 Key Points 592

20.8 Problems 593

21 Magnetic Materials Ⅱ:Microscopic View 595

21.1 Introduction 595

21.2 Jellium model and el-el Coulomb Repulsion 599

21.2.1 Is There Ferromagnetic Order in the JM? 599

21.2.2 Magnetic Susceptibility Within the JM in the Presence of Electron-Electron Interactions 601

21.2.3 Is There Antiferromagnetic Order in the JM? 603

21.3 The Hubbard Model 607

21.4 The Heisenberg Model 613

21.4.1 The Hamiltonian 613

21.4.2 Mean Field Approximation 615

21.4.3 The Ferromagnetic Case,(Jij>0)and its spin waves 617

21.4.4 The AF Case 619

21.5 Key Points 622

21.6 Problems 624

22 Superconductivity,Ⅰ:Phenomenology 625

22.1 Materials 625

22.2 Properties of Superconductors 627

22.2.1 Zero DC Resistivity 627

22.2.2 Expulsion of the Magnetic Field B from the Interior of a Superconductor 627

22.2.3 Critical Value of the Magnetic Field Beyond Which Superconductivity Disappears 629

22.2.4 Specific Heat and Other Thermodynamic Quantities 632

22.2.5 Response to Microwave or Far Infrared EM Radiation 634

22.2.6 Ultrasound Attenuation 635

22.2.7 Tunneling Current in Metal/Insulator/Superconductor Junctions 635

22.2.8 Temperature Dependence of the Superconducting Gap 635

22.2.9 Isotope Effect 637

22.2.10 Relaxation Times for Nuclear Spin 638

22.2.11 Thermoelectric Coefficients 638

22.3 Thermodynamic Relations 639

22.4 London Equation 641

22.5 Pippard's Generalization 644

22.6 Ginzburg-Landau Theory 645

22.7 Quantization of the Magnetic Flux 651

22.8 Key Points 652

22.9 Problems 654

23 Superconductivity,Ⅱ:Microscopic Theory 655

23.1 Electron-Electron Indirect Attraction 655

23.2 Cooper Pairs 657

23.3 Comments 659

23.4 Corrected Binding Energy and the Critical Temperature 661

23.5 Further Corrections to the Formula for Tc 663

23.6 The Bardeen-Cooper-Schrieffer(BCS)Theory 664

23.7 Thermodynamic Quantities 669

23.8 Response to Electromagnetic Fields 672

23.9 Towards Material-Specific Calculations of Superconducting Quantities 674

23.10 Josephson Effects and SQUID 677

23.11 Key Points 680

23.12 Problems 682

Part Ⅶ Appendices 685

A Elements of Electrodynamics of Continuous Media 685

A.1 Field Vectors,Potentials,and Maxwell's Equations 685

A.2 Relations Among the Fields 688

B Elements of Quantum Mechanics 697

B.1 General Formalism 697

B.2 Bra and Ket Notation 700

B.3 Spherically Symmetric Potentials 702

B.4 Perturbation Results 708

B.5 Interaction of Matter with an External Electromagnetic Field 711

C Elements of Thermodynamics and Statistical Mechanics 713

C.1 Thermodynamic Relations 713

C.2 Basic Relations of Statistical Mechanics 716

C.3 Non-Interacting Particles 718

C.3.1 Non-Interacting Electrons 718

C.3.2 Phonons 721

D Dielectric Function,ε(κ,ω):Formulas and Uses 723

D.1 Uses 724

D.2 Expressions for ε(κ,ω)within the JM 728

D.3 Phenomenological Expressions for the Dielectric Function 730

E Waves in Continuous Elastic Media 733

E.1 Strains 733

E.2 Equations of Motion 733

E.3 Connecting Stress and Strain 734

E.4 The Elastic Wave Equation 735

F The Method LCAO Applied to Molecules 737

F.1 Formulation of the LCAO Method 737

F.2 Some Important Examples 740

F.2.1 Covalent Diatomic Molecule 740

F.2.2 Ionic Diatomic Molecule 742

F.3 Hybridization of Atomic Orbitals 743

F.3.1 sp1 Hybrid Atomic Orbitals 744

F.3.2 sp2 Hybrid Atomic Orbitals 748

F.3.3 sp3 Hybrid Atomic Orbitals 749

G Boltzmann's Equation 755

H Tables 759

Solutions of Selected Problems and Answers 779

General Reading 826

References 837

Index 849