The study of solids is one of the richest, most exciting, and most successful branches of physics. While the subject of solid state physics is often viewed as dry and tedious this new book presents the topic instead as an exciting exposition of fundamental principles and great intellectual breakthroughs. Beginning with a discussion of how the study of heat capacity of solids ushered in the quantum revolution, the author presents the key ideas of the field while emphasizing the deep underlying concepts.

1 About Condensed Mattei·Physics 1

1.1 What Is Condensed Matter Physics 1

1.2 Why Do We Study Condensed Matter Physics? 1

1.3 Why Solid State Physics? 3

I Physics of Solids wi thou t Considering Micro- scopic Structure: The Early Days of Solid State 5

2 Specific Heat of Solids: Boltzmann, Einstein, and Debye 7

2.1 Einstein's Calculation

2.2 Debye's Calculation 9

      2.2.1 Periodic (Born-vo n Karman) Bow1dary Conditions 10

      2.2.2 Debye's Calculation Followi ng Planck 11

      2.2.3 Debye's “Interpolation” 13

      2.2.4 Some Shortcom ings of the Debye Theory 14

2.3 Appendix to th.is Chapter: ((4) 16

Exercises 17

3 Electrons in Metals: Drude Theory 19

3.1 Electrons in Fields 20

      3.1.1 Electrons in an Electric Field 20

      3.1.2 Electrons in Electric and Magnetic Fields 21

3.2 Thermal 'I'ransport 22

Exercises 25

4 More Electrons in Metals: Sommerfeld (Free Electron) Theory 27

4.1 Basic Fermi- Dirac Statistics 27

4.2 Electronic Heat Capacity 29

4.3 Magnetic Spin Susceptibility (Pauli Paramagnetism) 32

4.4 Why Drude Theory Works So Well 34

4.5 Shortcomi ngs of the Free Electron Model 35

Exercises 37

II Structure of Materials 39

5 The Periodic Table 41

5.1 Chcmist,ry, Atoms, and the Schroed i nger Equation 41

5.2 Structure of the Periodic Table 42

5.3 Periodic Tend 43

      5.3.1 Effective Nuclear Charge 45

      Exercises 46

6 What Holds Solids Together: Chemical Bonding 49

6.1 Ionic Bonds 49

6.2 Covalent Bond 52

      6.2.1 Particle i n a Box Pictu re 52

      6.2.2 Molecu lar Orbital or Tight Binding Theory 53

6.3 Van der \Naals, Fluctuating Dipole Forces, or Molecular Bonding 57

6.4 Metallic Bond i ng 59

6.5 Hydrogen Bonds 59

Exercises 61

7 Types of Matter 65

III Toy Models of Solids in One Dimension 69

8 One-Dimensional Model of Compressibility, Sound, and Thermal Expansion 71

Exercises 74

9 Vibrations of a One-Dimensional Monatomic Chain 77

9.1 First Exposure to the Reciprocal Lattice 79

9.2 Properties of the Dispersion of the One-Dimensional Chain 80

9.3 Quantum Jvlodes: Phonons 82

9.4 Crystal Momentum 84

Exercises 86

10 Vibrations of a One-Dimensional Diatomic Chain 89

10.1 Diatomic Crystal Structure: Some Useful Definitions 89

10.2 Norm al Nifodes of the Diatomic Solid 90

Exercises 96

11 Tight Binding Chain (Interlude and Preview) 99

11.1 Tight Binding Model in One Dimension 99

11.2 Solution of the Tight Binding Chain 101

11.3 Introduction to Electrons Filling Bands 104

11.4 Multiple Bands 105

Exercises 107

IV Geometry of Solids 111

12 Crystal Structure 113

12.1 Lattices and Unit Cells 113

12.2 Lattices in Th ree Dimensions 117

      12.2.1 The Body-Centered Cubic (bee) Lattice 118

      12.2.2 The Face-Centered Cubic (fee) Lattice 120

      12.2.3 Sphere Packi ng 121

      12.2.4 OLher Lattices in Three Dimensions 122

      12.2.5 Some Real Crystals 123

Exercises 125

13 Reciprocal Lattice, Brilloui n Zone, Waves in Crystals 127

13.1 The Reciprocal Lattice in Three Dimensions 127

      13.1.1 Review of One Dimension 127

      13.1.2 R eci procal LaUice Definition 128

      13.1.3 The Reci procal LaUice as a Fou rier Transform 129

      13.1.4 n eci procal Lattice Points as Families of Lattice Planes 130

      13.1.5 LaUice Planes and Mi ller Indices 132

13.2 Bri llouin Zones 134

      13.2.1 R eview of One-Di mensional Dispersions and Bril louin Zones 134

      13.2.2 General Bri llouin Zone Construction 134

13.3 Electron ic and Vi brational Waves in Crystals in Three Dimensions 136

Exercises 137

V Neutron and X-Ray Diffraction 139

14 Wave Scattering by Crystals 141

14.1 The Laue and Bragg Cond i tions 141

      14.1.1 Fermi 's Golden Rule Approach 141

      14.1.2 Diffraction Approach 142

      14.1.3 Equivalence of Laue and Bragg conditions 143

14.2 Scattering Amplitudes 144

      14.2.1 Simple Exam ple 146

      14.2.2 Systematic Absences and Ntlore Example 147

      14.2.3 Geometric Interpretation of Selection Rules 149

14.3 Methods of Scattering Experi ments 150

      14.3.1 Advanced Methods 150

      14.3.2 Powd er Diffraction 151

14.4 Still More Abou t Scatteri ng 156

      14.4.1 Scattering in Liquids and Amorph ous Solids 156

      14.4.2 Variant: Inelastic Scattering 156

      14.4.3 Exper imental Apparatus 157

Exercise 159

VI Electrons in Solids 161

15 Electrons in a Period ic Potential 163

15.1 Nearly Free Electron Model 163

      15.1.1 Degenerate Pertu rbation Theory 165

15.2 Bloch's Theorem 169

Exercises 171

16 Insulator, Semiconductor, or Metal 173

16.1 Energy Bands i n One Dimension 173

16.2 Energy Ba11ds in Two and Three Dimensions 175

16.3 Tight Binding 177

16.4 Failu res of the Band-Structure Picture of Metals and Insulators 177

16.5 Band Structure and Optical Properties 179

      16.5.1 Optical Properties of Insulators and Semicond uctors 179

      16.5.2 Direct and Indirect Transitions 179

      16.5.3 Optical Properties of Nietals 180

      16.5.4 Optical Effects of Impurities 181

      Exercises 182

17 Semiconductor Physics 183

17.1 Electrons and Hole: 183

      17.1.1 Drude Transport: Redux 186

17.2 Addi ng Electrons or Holes with Impurities: Doping 187

      17.2.1 Lnpw-ity States 188

17.3 Statistical Mechanics of Semicond uctors 191

Exercises 195

18 Semiconductor Devices 197

18.1 Band Structure Engineering 197

      18.1.1 Designing Band Gaps 197

      18.1.2 Non-Homogeneous Band Gaps 198

18.2 p-π Junction 199

18.3 The Transistor 203

Exercises 205

VII Magnet ism and Mean Field Theories 207

19 Magnetic Properties of Atoms: Para- and Dia-Magnetism 209

19.1 Basic Definitions of Types of 1/fagnetisrn 209

19.2 Atomic Physics: Hund 's Rules 211

      19.2.1 Why Moments Align 212

19.3 Coupling of Electrons i n Atoms to an External Field 214

19.4 Free Spin (Curie or Langevin) Paramagnetism 215

19.5 Larrnor Diamagnetism 217

19.6 Atoms in Solids 218

      19.6.1 Pauli Paramagnetism in Mctals219

      19.6.2 Diamagnetismin Solid 219

      19.6.3 Curie Paramagnetism in Solids 220

Exercises 222

20 Spontaneous Magnetic Order: Ferro-, Antiferro- , and Ferri-Magnetism 225

20.1 (Spontaneous) Magnetic Order 226

      20.1.1 Ferromagnets 226

      20.1.2 Antifcrromagnets 226

      20.1.3 Ferri magnets 227

20.2 Breaking Symmetry 228

      20.2.1 Ising Model 228

Exercises 229

21 Domains and Hysteresis 233

21.1 Macroscopic Effects in Ferromagnets: Domains 233

      21.1.1 Domain Wall Structu re and the Bloch/ Neel Wall 234

21.2 Hyst.eresis in Fcrromagn ets 236

      21.2.1 Disorder Pinning 236

      21.2.2 Single-Domain CrysLallites 236

      21.2.3 Domai n Pin ning and Hyster℃sis 23

Exercises 240

22 Mean Field Theory 243

22.1 Mean Field Equations for the Ferrom agnetic Ising 243

22.2 Solu tion of Self-Consistency Equation 245

      22.2.1 Paramagnetic Susceptibility 246

      22.2.2 Further Thoughts 247

      Exercises 248

23 Magnetism from Interactions: The Hubbard Model 251

23.1 Itinerant Ferrom agnetism 252

      23.1.1 Hu bbard Ferromagnetism Mean Field Theory 252

      23.1.2 Stoner Criterion 253

23.2 Mott Antiferrom agnetism 255

23.3 Appendix: Hu bbard Model for the Hydrogen Molecule 257

Exercises 259

A Sample Exam and Solutions 261

B List of Other Good Books 275

Indices 279

Index of People 280

Index of Topics 283

Steven H. Simon, Professor of Theoretical Condensed Matter Physics, Department of Physics, University of Oxford, and Fellow of Somerville College, Oxford.PA\Professor Steven Simon earned a BSc degree from Brown in Physics & Mathematics in 1989 and a PhD in Theoretical Physics from Harvard in 1995. Following a two-year post-doc at MIT, he joined Bell Labs, where he was a director of research for nine years. He is currently Professor of Theoretical Condensed Matter Physics in the Department of Physics at the University of Oxford, and a Fellow of Somerville College, Oxford. His research is in the area of condensed matter physics and communication, including subjects ranging from microwave propagation to high temperature superconductivity. He is interested in quantum effects and how they are manifested in phases of matter. He has recently been studying phases of matter known as "topological phases" that are invariant under smooth deformations of space-time. He is also interested in whether such phases of matter can be used for quantum information processing and quantum computation.

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