Condensed Matter In a Nutshell (ebook)

Argumento de Condensed Matter In a Nutshell (ebook)

"Mahan's book does an admirable job of covering the broad subject of condensed matter physics in a balanced way. Virtually every important modern topic is explained. The informal narrative style gives the reader the sense of sitting in on a lecture by the master. The long search for a suitable text for a one-year graduate course on condensed matter physics may finally be over."--Patrick A. Lee, Massachusetts Institute of Technology

"This book is a great place to start learning about the vast array of phenomena that nature is able to produce around us in the form of materials. It hardly fits in a nutshell--it covers a great many topics, both traditional and current, in condensed matter physics. It is more akin to Hamlet's assertion that he could be bounded in a nutshell, and count himself a king of infinite space. The prodigious knowledge of the author shines through in the choice of topics."--Sidney R. Nagel, University of Chicago

"This is an excellent book that shows the author's wide grasp of the material. I particularly appreciate the many problems at the end of each chapter. Another welcome feature is the inclusion of many hot, still-developing topics in contemporary solid state physics."--Torgny Gustafsson, Rutgers University

"Mahan is a nuts-and-bolts theorist. Condensed Matter in a Nutshell includes many current hot topics, and the problem sets are well chosen. The book will help those trained in chemistry and materials science, both professionals and students, to come to grips with the current thinking in condensed matter physics, and it directs readers where to go for deeper immersion."--Zachary Fisk, University of California, Irvine

"Don't skip the introduction. It will not only re-energize those synapses which remember the history of chemistry, geology, and crystal growth, but it also poses some apparently simple questions which reveal the thrust of modern material research--all in eight pages."--Bruce L. Dietrich, Planetarian0Preface xiii
Chapter 1: Introduction 1
1.1 1900-1910 1
1.2 Crystal Growth 2
1.3 Materials by Design 4
1.4 Artificial Structures 5

Chapter 2: Crystal Structures 9
2.1 Lattice Vectors 9
2.2 Reciprocal Lattice Vectors 11
2.3 Two Dimensions 13
2.4 Three Dimensions 15
2.5 Compounds 19
2.6 Measuring Crystal Structures 21
2.6.1 X-ray Scattering 22
2.6.2 Electron Scattering 23
2.6.3 Neutron Scattering 23
2.7 Structure Factor 25
2.8 EXAFS 26
2.9 Optical Lattices 28

Chapter 3: Emergy Bands 31
3.1 Bloch's Theorem 31
3.1.1 Floquet's Theorem 32
3.2 Nearly Free Electron Bands 36
3.2.1 Periodic Potentials 36
3.3 Tight-binding Bands 38
3.3.1 s-State Bands 38
3.3.2 p-State Bands 41
3.3.3 Wannier Functions 43
3.4 Semiconductor Energy Bands 44
3.4.1 What Is a Semiconductor? 44
3.4.2 Si, Ge, GaAs 47
3.4.3 HgTe and CdTe 50
3.4.4 k · p Theory 51
3.4.5 Electron Velocity 55
3.5 Density of States 55
3.5.1 Dynamical Mean Field Theory 58
3.6 Pseudopotentials 60
3.7 Measurement of Energy Bands 62
3.7.1 Cyclotron Resonance 62
3.7.2 Synchrotron Band Mapping 63

Chapter 4: Insulators 68
4.1 Rare Gas Solids 68
4.2 Ionic Crystals 69
4.2.1 Madelung energy 71
4.2.2 Polarization Interactions 72
4.2.3 Van der Waals Interaction 75
4.2.4 Ionic Radii 75
4.2.5 Repulsive Energy 76
4.2.6 Phonons 77
4.3 Dielectric Screening 78
4.3.1 Dielectric Function 78
4.3.2 Polarizabilities 80
4.4 Ferroelectrics 82
4.4.1 Microscopic Theory 83
4.4.2 Thermodynamics 87
4.4.3 SrTiO3 89
4.4.4 BaTiO3 91

Chapter 5: Free Electron Metals 94
5.1 Introduction 94
5.2 Free Electrons 96
5.2.1 Electron Density 96
5.2.2 Density of States 97
5.2.3 Nonzero Temperatures 98
5.2.4 Two Dimensions 101
5.2.5 Fermi Surfaces 102
5.2.6 Thermionic Emission 104
5.3 Magnetic Fields 105
5.3.1 Integer Quantum Hall Effect 107
5.3.2 Fractional Quantum Hall Effect 110
5.3.3 Composite Fermions 113
5.3.4 deHaas-van Alphen Effect 113
5.4 Quantization of Orbits 117
5.4.1 Cyclotron Resonance 119

Chapter 6: Electron-Electron Interactions 127
6.1 Second Quantization 128
6.1.1 Tight-binding Models 131
6.1.2 Nearly Free Electrons 131
6.1.3 Hartree Energy: Wigner-Seitz 134
6.1.4 Exchange Energy 136
6.1.5 Compressibility 138
6.2 Density Operator 141
6.2.1 Two Theorems 142
6.2.2 Equations of Motion 143
6.2.3 Plasma Oscillations 144
6.2.4 Exchange Hole 146
6.3 Density Functional Theory 148
6.3.1 Functional Derivatives 149
6.3.2 Kinetic Energy 150
6.3.3 Kohn-Sham Equations 151
6.3.4 Exchange and Correlation 152
6.3.5 Application to Atoms 154
6.3.6 Time-dependent Local Density Approximation 155
6.3.7 TDLDA in Solids 157
6.4 Dielectric Function 158
6.4.1 Random Phase Approximation 159
6.4.2 Properties of P (q, w) 161
6.4.3 Hubbard-Singwi Dielectric Functions 164
6.5 Impurities in Metals 165
6.5.1 Friedel Analysis 166
6.5.2 RKKY Interaction 170

Chapter 7: Phonons 176
7.1 Phonon Dispersion 176
7.1.1 Spring Constants 177
7.1.2 Example: Square Lattice 179
7.1.3 Polar Crystals 181
7.1.4 Phonons 181
7.1.5 Dielectric Function 185
7.2 Phonon Operators 187
7.2.1 Simple Harmonic Oscillator 187
7.2.2 Phonons in One Dimension 189
7.2.3 Binary Chain 192
7.3 Phonon Density of States 195
7.3.1 Phonon Heat Capacity 197
7.3.2 Isotopes 199
7.4 Local Modes 203
7.5 Elasticity 205
7.5.1 Stress and Strain 205
7.5.2 Isotropic Materials 208
7.5.3 Boundary Conditions 210
7.5.4 Defect Interactions 211
7.5.5 Piezoelectricity 214
7.5.6 Phonon Focusing 215
7.6 Thermal Expansion 216
7.7 Debye-Waller Factor 217
7.8 Solitons 220
7.8.1 Solitary Waves 220
7.8.2 Cnoidal Functions 222
7.8.3 Periodic Solutions 223

Chapter 8: Boson Systems 230
8.1 Second Quantization 230
8.2 Superfluidity 232
8.2.1 Bose-Einstein Condensation 232
8.2.2 Bogoliubov Theory of Superfluidity 234
8.2.3 Off-diagonal Long-range Order 240
8.3 Spin Waves 244
8.3.1 Jordan-Wigner Transformation 245
8.3.2 Holstein-Primakoff Transformation 247
8.3.3 Heisenberg Model 248

Chapter 9: Electron-Phonon Interactions 254
9.1 Semiconductors and Insulators 254
9.1.1 Deformation Potentials 255
9.1.2 Fröhlich Interaction 257
9.1.3 Piezoelectric Interaction 258
9.1.4 Tight-binding Models 259
9.1.5 Electron Self-energies 260
9.2 Electron-Phonon Interaction in Metals 263
9.2.1 ? 264
9.2.2 Phonon Frequencies 267
9.2.3 Electron-Phonon Mass Enhancement 268
9.3 Peierls Transition 272
9.4 Phonon-mediated Interactions 276
9.4.1 Fixed Electrons 276
9.4.2 Dynamical Phonon Exchange 278
9.5 Electron-Phonon Effects at Defects 281
9.5.1 F-Centers 281
9.5.2 Jahn-Teller Effect 284

Chapter 10: Extrinsic Semiconductors 287
10.1 Introduction 287
10.1.1 Impurities and Defects in Silicon 288
10.1.2 Donors 289
10.1.3 Statistical Mechanics of Defects 292
10.1.4 n-p Product 294
10.1.5 Chemical Potential 295
10.1.6 Schottky Barriers 297
10.2 Localization 301
10.2.1 Mott Localization 301
10.2.2 Anderson Localization 304
10.2.3 Weak Localization 304
10.2.4 Percolation 306
10.3 Variable Range Hopping 310
10.4 Mobility Edge 311
10.5 Band Gap Narrowing 312

Chapter 11: Transport Phenomena 320
11.1 Introduction 320
11.2 Drude Theory 321
11.3 Bloch Oscillations 322
11.4 Boltzmann Equation 324
11.5 Currents 327
11.5.1 Transport Coefficients 327
11.5.2 Metals 329
11.5.3 Semiconductors and Insulators 333
11.6 Impurity Scattering 335
11.6.1 Screened Impurity Scattering 336
11.6.2 T-matrix Description 337
11.6.3 Mooij Correlation 338
11.7 Electron-Phonon Interaction 340
11.7.1 Lifetime 341
11.7.2 Semiconductors 343
11.7.3 Saturation Velocity 344
11.7.4 Metals 347
11.7.5 Temperature Relaxation 348
11.8 Ballistic Transport 350
11.9 Carrier Drag 353
11.10 Electron Tunneling 355
11.10.1 Giaever Tunneling 356
11.10.2 Esaki Diode 358
11.10.3 Schottky Barrier Tunneling 361
11.10.4 Effective Mass Matching 362
11.11 Phonon Transport 364
11.11.1 Transport in Three Dimensions 364
11.11.2 Minimum Thermal Conductivity 365
11.11.3 Kapitza Resistance 366
11.11.4 Measuring Thermal Conductivity 368
11.12 Thermoelectric Devices 370
11.12.1 Maximum Cooling 371
11.12.2 Refrigerator 373
11.12.3 Power Generation 374

Chapter 12: Optical Properties 379
12.1 Introduction 379
12.1.1 Optical Functions 379
12.1.2 Kramers-Kronig Analysis 381
12.2 Simple Metals 383
12.2.1 Drude 383
12.3 Force-Force Correlations 385
12.3.1 Impurity Scattering 386
12.3.2 Interband Scattering 388
12.4 Optical Absorption 389
12.4.1 Interband Transitions in Insulators 389
12.4.2 Wannier Excitons 392
12.4.3 Frenkel Excitons 395
12.5 X-Ray Edge Singularity 396
12.6 Photoemission 399
12.7 Conducting Polymers 401
12.8 Polaritons 404
12.8.1 Phonon Polaritons 404
12.8.2 Plasmon Polaritons 405
12.9 Surface Polaritons 406
12.9.1 Surface Plasmons 408
12.9.2 Surface Optical Phonons 410
12.9.3 Surface Charge Density 413

Chapter 13: Magnetism 418
13.1 Introduction 418
13.2 Simple Magnets 418
13.2.1 Atomic Magnets 418
13.2.2 Hund's Rules 418
13.2.3 Curie's Law 420
13.2.4 Ferromagnetism 422
13.2.5 Antiferromagnetism 423
13.3 3d Metals 424
13.4 Theories of Magnetism 425
13.4.1 Ising and Heisenberg Models 425
13.4.2 Mean Field Theory 427
13.4.3 Landau Theory 431
13.4.4 Critical Phenomena 433
13.5 Magnetic Susceptibility 434
13.6 Ising Model 436
13.6.1 One Dimension 436
13.6.2 Two and Three Dimensions 437
13.6.3 Bethe Lattice 439
13.6.4 Order-Disorder Transitions 443
13.6.5 Lattice Gas 445
13.7 Topological Phase Transitions 446
13.7.1 Vortices 447
13.7.2 XY-Model 448
13.8 Kondo Effect 452
13.8.1 sd-Interaction 453
13.8.2 Spin-flip Scattering 454
13.8.3 Kondo Resonance 456
13.9 Hubbard Model 458
13.9.1 U = 0 Solution 459
13.9.2 Atomic Limit 460
13.9.3 U > 0 460
13.9.4 Half-filling 462

Chapter 14: Superconductivity 467
14.1 Discovery of Superconductivity 467
14.1.1 Zero resistance 467
14.1.2 Meissner Effect 468
14.1.3 Three Eras of Superconductivity 469
14.2 Theories of Superconductivity 473
14.2.1 London Equation 473
14.2.2 Ginzburg-Landau Theory 475
14.2.3 Type II 478
14.3 BCS Theory 479
14.3.1 History of Theory 479
14.3.2 Effective Hamiltonian 480
14.3.3 Pairing States 481
14.3.4 Gap Equation 483
14.3.5 d-Wave Energy Gaps 486
14.3.6 Density of States 487
14.3.7 Ultrasonic Attenuation 489
14.3.8 Meissner Effect 490
14.4 Electron Tunneling 492
14.4.1 Normal-Superconductor 494
14.4.2 Superconductor-Superconductor 497
14.4.3 Josephson Tunneling 498
14.4.4 Andreev Tunneling 501
14.4.5 Corner Junctions 502
14.5 Cuprate Superconductors 503
14.5.1 Muon Rotation 503
14.5.2 Magnetic Oscillations 506
14.6 Flux Quantization 507

Chapter 15: Nanometer Physics 511
15.1 Quantum Wells 512
15.1.1 Lattice Matching 512
15.1.2 Electron States 513
15.1.3 Excitons and Donors in Quantum Wells 515
15.1.4 Modulation Doping 518
15.1.5 Electron Mobility 520
15.2 Graphene 520
15.2.1 Structure 521
15.2.2 Electron Energy Bands 522
15.2.3 Eigenvectors 525
15.2.4 Landau Levels 525
15.2.5 Electron-Phonon Interaction 526
15.2.6 Phonons 528
15.3 Carbon Nanotubes 530
15.3.1 Chirality 530
15.3.2 Electronic States 531
15.3.3 Phonons in Carbon Nanotubes 536
15.3.4 Electrical Resistivity 537

Appendix 541
Index 553