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Condensed Matter Physics (seems comprehensive)
Michael Marder
Center for Nonlinear Dynamics, University of Texas, Austin
TABLE OF CONTENTS
PART I: ATOMIC STRUCTURE
Chapter 1: The Idea of Crystals, page 3
1.1, Introduction, page 3
1.1.1, Why are Solids Crystalline?, page 4
1.2, Two-Dimensional Lattices, page 6
1.2.1, Bravais Lattices, page 6
1.2.2, Enumeration of Two-Dimensional Bravais Lattices, page 7
1.2.3, Lattices with Bases, page 7
1.2.4, Primitive Cells, page 9
1.2.5, Wigner--Seitz Cells, page 10
1.3, Symmetries, page 11
1.3.1, The Space Group, page 11
1.3.2, Translation and Point Groups, page 11
Problems, page 13
References, page 15
Chapter 2: Three-Dimensional Lattice, page 17
2.1, Introduction, page 17
2.1.1, Distribution Among Elements, page 17
2.2, Monatomic Lattices, page 20
2.2.1, The Simple Cubic Lattice, page 20
2.2.2, The Face-Centered Cubic Lattice, page 20
2.2.3, The Body-Centered Cubic Lattice, page 21
2.2.4, The Hexagonal Lattice, page 22
2.2.5, The Hexagonal Close-Packed Lattice, page 23
2.2.6, The Diamond Lattice, page 24
2.3, Compounds , page 24
2.3.1, Rocksalt---Sodium Chloride, page 25
2.3.2, Cesium Chloride, page 26
2.3.3, Fluorite---Calcium Fluoride, page 26
2.3.4, Zincblende---Zinc Sulfide, page 26
2.3.5, Wurtzite---Zinc Oxide, page 28
2.3.6, Perovskite---Calcium Titanate , page 28
2.4, Classification of Lattices by Symmetry, page 28
2.4.1, Fourteen Bravais Lattices and Seven Crystal Systems, page 30
2.5, Symmetries of Lattices with Bases, page 32
2.5.1, Thirty-Two Crystallographic Point Groups, page 32
2.5.2, Two Hundred Thirty Distinct Lattices, page 36
2.6, Some Macroscopic Implications of Microscopic Symmetries, page 37
2.6.1, Pyroelectricity, page 37
2.6.2, Piezoelectricity, page 37
2.6.3, Optical Activity, page 38
Problems, page 38
References, page 41
Chapter 3: Experimental Determination of Crystal Structure, page 43
3.1, Introduction, page 43
3.2, Theory of Scattering from Crystals, page 44
3.2.1, Lattice Sums, page 47
3.2.2, Reciprocal Lattice, page 48
3.2.3, Miller Indices, page 51
3.2.4, Scattering from a Lattice with a Basis, page 52
3.3, Experimental Methods, page 54
3.3.1, Laue Method, page 55
3.3.2, Rotating Crystal Method, page 56
3.3.3, Powder Method, page 58
3.4, Further Features of Scattering Experiments, page 59
3.4.1, Interaction of X-Rays with Matter, page 60
3.4.2, Production of X-Rays, page 60
3.4.3, Neutrons, page 61
3.4.4, Electrons, page 61
3.4.5, Deciphering Complex Structures, page 63
3.4.6, Accuracy of Structure Determinations, page 64
Problems, page 65
References, page 67
Chapter 4: Surfaces and Interface, page 69
4.1, Introduction, page 69
4.2, Geometry of Interfaces, page 69
4.2.1, Coherent and Commensurate Interfaces, page 70
4.2.2, Stacking Period and Interplanar Spacing, page 71
4.2.3, Other Topics in Surface Structure, page 73
4.3, Experimental Observation and Creation of Surfaces, page 73
4.3.1, Low-Energy Electron Diffraction (LEED), page 74
4.3.2, Reflection High-Energy Electron Diffraction (RHEED), page 75
4.3.3, Molecular Beam Epitaxy (MBE), page 76
4.3.4, Field Ion Microscopy (FIM), page 77
4.3.5, Scanning Tunneling Microscopy (STM), page 77
4.3.6, Atomic Force Microscopy (AFM), page 82
4.3.7, High Resolution Electron Microscopy (HREM), page 82
Problems, page 82
References, page 85
Chapter 5: Complex Structure, page 87
5.1, Introduction, page 87
5.2, Alloys, page 87
5.2.1, Equilibrium Structures, page 87
5.2.2, Phase Diagrams, page 89
5.2.3, Superlattices, page 90
5.2.4, Phase Separation, page 91
5.2.5, Nonequilibrium Structures in Alloys, page 94
5.2.6, Dynamics of Phase Separation, page 95
5.3, Simulations, page 97
5.3.1, Monte Carlo, page 97
5.3.2, Molecular Dynamics, page 98
5.4, Liquids, page 99
5.4.1, Correlation Functions, page 99
5.4.2, Extended X-Ray Absorption Fine Structure (EXAFS), page 101
5.4.3, Calculating Correlation Functions, page 103
5.5, Glasses, page 103
5.6, Liquid Crystals, page 107
5.6.1, Nematics, Cholesterics, and Smectics, page 108
5.6.2, Liquid Crystal Order Parameter, page 109
5.7, Polymers, page 110
5.7.1, Ideal Radius of Gyration, page 111
5.8, Quasicrystals, page 115
5.8.1, One-Dimensional Quasicrystal, page 116
5.8.2, Two-Dimensional Quasicrystals---Penrose Tiles, page 121
5.8.3, Experimental Observations, page 124
5.8.4, Fullerenes, page 124
Problems, page 125
References, page 129
PART II: ELECTRONIC STRUCTURE
Chapter 6: The Single-Electron Model, page 135
6.1, Introduction, page 135
6.2, The Basic Hamiltonian, page 137
6.3, Densities of States, page 139
6.3.1, Definition of Density of States ${D, page {140}
6.3.2, Results for Free Electrons, page 141
6.4, Statistical Mechanics of Noninteracting Electrons, page 143
6.5, Sommerfeld Expansion, page 146
6.5.1, Specific Heat of Noninteracting Electrons at Low Temperatures , page 149
Problems, page 150
References, page 153
Chapter 7: The Schroedinger Equation and Symmetry, page 155
7.1, Introduction, page 155
7.2, Translational Symmetry---Bloch's Theorem, page 155
7.2.1, Van Hove Singularities, page 160
7.2.2, Fourier Analysis of Bloch's Theorem, page 163
7.2.3, Kronig--Penney Model, page 166
7.3, Rotational Symmetry---Group Representations, page 169
7.3.1, Classes and Characters, page 175
7.3.2, Consequences of point group symmetries for Schr\"odinger's equation, page 178
Problems, page 181
References, page 184
Chapter 8: Nearly Free and Tightly Bound Electrons, page 185
8.1, Introduction, page 185
8.2, Nearly Free Electrons, page 185
8.2.1, Degenerate Perturbation Theory, page 187
8.3, Brillouin Zones, page 189
8.3.1, Nearly Free Electron Fermi Surfaces, page 191
8.4, Tightly Bound Electrons, page 194
8.4.1, Wannier Functions, page 194
8.4.2, Tight Binding Model, page 197
Problems, page 199
References, page 202
Chapter 9: Electron--Electron Interactions, page 203
9.1, Introduction, page 203
9.2, Hartree and Hartree--Fock Equations, page 204
9.2.1, Variational Principle, page 205
9.2.2, Hartree--Fock Equations, page 205
9.2.3, Numerical Implementation, page 209
9.2.4, Hartree--Fock Equations for Jellium, page 212
9.3, Density Functional Theory, page 214
9.3.1, Thomas--Fermi Theory, page 216
9.3.2, Kohn--Sham Equations, page 218
9.4, Stability of Matter, page 220
Problems, page 223
References, page 226
Chapter 10: Calculation of Band Structures, page 229
10.1, Introduction, page 229
10.2, Numerical Methods, page 230
10.2.1, Pseudopotentials and Orthogonalized Planes Waves (OPW), page 230
10.2.2, Linear Combination of Atomic Orbitals (LCAO), page 235
10.2.3, Plane Waves, page 237
10.2.4, Linear Augmented Plane Waves (LAPW), page 240
10.2.5, Linearized Muffin Tin Orbitals (LMTO), page 243
10.3, Definition of Metals, Insulators, and Semiconductors, page 246
10.4, Brief Survey of the Periodic Table, page 248
10.4.1, Noble Gases, page 248
10.4.2, Nearly Free Electron Metals, page 250
10.4.3, Semiconductors, page 252
10.4.4, Transition Metals, page 252
10.4.5, Rare Earths, page 252
Problems, page 254
References, page 258
PART III: MECHANICAL PROPERTIES
Chapter 11: Cohesion of Solids, page 263
11.1, Introduction, page 263
11.1.1, Radii of Atoms, page 263
11.2, Noble Gases, page 265
11.3, Ionic Crystals, page 269
11.3.1, Ewald Sums, page 270
11.4, Metals, page 272
11.4.1, Use of Pseudopotentials, page 275
11.5, Band Structure Energy, page 276
11.5.1, Peierls Distortion, page 277
11.5.2, Structural Phase Transitions, page 279
11.6, Hydrogen-Bonded Solids, page 280
11.7, Cohesive Energy from Band Calculations, page 280
11.8, Classical Potentials, page 282
Problems, page 283
References, page 285
Chapter 12: Elasticity, page 287
12.1, Introduction, page 287
12.2, General Theory of Linear Elasticity , page 287
12.2.1, Solids of Cubic Symmetry, page 289
12.2.2, Isotropic Solids, page 290
12.3, Other Constitutive Laws, page 295
12.3.1, Liquid Crystals, page 295
12.3.2, Rubber, page 298
12.3.3, Composite and Granular Materials, page 301
Problems, page 301
References, page 303
Chapter 13: Phonons , page 305
13.1, Introduction, page 305
13.2, Vibrations of a Classical Lattice, page 305
13.2.1, Normal Modes, page 307
13.2.2, Lattice with a Basis, page 309
13.3, Vibrations of a Quantum--Mechanical Lattice, page 313
13.3.1, Phonon Specific Heat, page 317
13.3.2, Einstein and Debye Models, page 321
13.3.3, Thermal Expansion, page 324
13.4, Inelastic Scattering from Phonons, page 326
13.4.1, Neutron Scattering, page 327
13.4.2, Formal Theory of Neutron Scattering, page 329
13.4.3, Averaging Exponentials, page 333
13.4.4, Evaluation of Structure Factor, page 335
13.4.5, Kohn Anomalies, page 336
13.5, The M\"ossbauer Effect, page 336
Problems, page 339
References, page 340
Chapter 14: Dislocations and Cracks, page 343
14.1, Introduction, page 343
14.2, Dislocations, page 345
14.2.1, Experimental Observations of Dislocations, page 347
14.2.2, Force to Move a Dislocation, page 350
14.2.3, One-Dimensional Dislocations: Frenkel--Kontorova Model, page 350
14.3, Two-Dimensional Dislocations and Hexatic Phases, page 353
14.3.1, Impossibility of Crystalline Order in Two Dimensions, page 353
14.3.2, Orientational Order, page 355
14.3.3, Kosterlitz--Thouless--Berezinskii Transition, page 356
14.4, Cracks, page 363
14.4.1, Fracture of a Strip, page 363
14.4.2, Stresses Around an Elliptical Hole, page 366
14.4.3, Stress Intensity Factor, page 368
14.4.4, Atomic Aspects of Fracture, page 368
Problems, page 370
References, page 373
Chapter 15: Fluid Mechanics, page 375
15.1, Introduction, page 375
15.2, Newtonian Fluids, page 375
15.2.1, Euler's Equation, page 375
15.2.2, Navier--Stokes Equation, page 377
15.3, Polymeric Solutions, page 378
15.4, Plasticity, page 385
15.5, Superfluid $^4$He, page 389
15.5.1, Two-Fluid Hydrodynamics, page 392
15.5.2, Second Sound, page 393
15.5.3, Origin of Superfluidity, page 395
15.5.4, Lagrangian Theory of Wave Function, page 400
15.5.5, Superfluid 3He, page 403
Problems, page 404
References, page 408
PART IV: ELECTRON TRANSPORT
Chapter 16: Dynamics of Bloch Electrons, page 413
16.1, Introduction, page 413
16.1.1, Drude Model, page 413
16.2, Semiclassical Electron Dynamics, page 415
16.2.1, Bloch Oscillations, page 416
16.2.2, k . P Method, page 417
16.2.3, Effective Mass, page 419
16.3, Noninteracting Electrons in an Electric Field, page 419
16.3.1, Zener Tunneling, page 422
16.4, Semiclassical Equations from Wave Packets, page 425
16.4.1, Formal Dynamics of Wave Packets, page 425
16.5, Quantizing Semiclassical Dynamics, page 430
16.5.1, Wannier--Stark Ladders, page 432
16.5.2, de Haas--van Alphen Effect, page 432
16.5.3, Experimental Measurements of Fermi Surfaces, page 434
Problems, page 437
References, page 440
Chapter 17: Transport Phenomena and Fermi Liquid Theory, page 443
17.1, Introduction, page 443
17.2, Boltzmann Equation, page 443
17.2.1, Boltzmann Equation, page 445
17.2.2, Relaxation Time Approximation, page 446
17.2.3, Relation to Rate of Production of Entropy, page 448
17.3, Transport Symmetries, page 449
17.3.1, Onsager Relations, page 450
17.4, Thermoelectric Phenomena, page 451
17.4.1, Electrical Current, page 451
17.4.2, Effective Mass and Holes, page 453
17.4.3, Mixed Thermal and Electrical Gradients, page 454
17.4.4, Wiedemann--Franz Law, page 455
17.4.5, Thermopower---Seebeck Effect, page 456
17.4.6, Peltier Effect, page 457
17.4.7, Thomson Effect, page 457
17.4.8, Hall Effect, page 459
17.4.9, Magnetoresistance, page 461
17.4.10, Giant Magnetoresistance, page 462
17.5, Fermi Liquid Theory, page 462
17.5.1, Basic Ideas, page 462
17.5.2, Statistical Mechanics of Quasi-Particles, page 464
17.5.3, Effective Mass, page 466
17.5.4, Specific Heat, page 468
17.5.5, Fermi Liquid Parameters, page 469
17.5.6, Traveling Waves, page 470
17.5.7, Comparison with Experiment in 3He, page 473
Problems, page 474
References, page 478
Chapter 18: Microscopic Theories of Conduction, page 481
18.1, Introduction, page 481
18.2, Weak Scattering Theory of Conductivity, page 481
18.2.1, General Formula for Relaxation Time, page 481
18.2.2, Matthiessen's Rule, page 486
18.2.3, Fluctuations, page 487
18.3, Metal--Insulator Transitions, page 488
18.3.1, Types of Impurities, page 488
18.3.2, Impurity Scattering and Green's Functions , page 492
18.3.3, Green's Functions, page 493
18.3.4, Single Impurity, page 497
18.4, Coherent Potential Approximation, page 499
18.5, Localization, page 500
18.5.1, Exact Results in One Dimension, page 501
18.5.2, Scaling Theory of Localization, page 505
18.5.3, Comparison with Experiment, page 509
Problems, page 510
References, page 514
Chapter 19: Electronics, page 517
19.1, Introduction, page 517
19.2, Metal Interfaces, page 518
19.2.1, Work Functions, page 519
19.2.2, Schottky Barrier, page 520
19.2.3, Contact Potentials, page 522
19.3, Semiconductors, page 524
19.3.1, Pure Semiconductors, page 525
19.3.2, Semiconductor in Equilibrium, page 528
19.3.3, Intrinsic Semiconductor, page 530
19.3.4, Extrinsic Semiconductor, page 531
19.4, Diodes and Transistors, page 533
19.4.1, Surface States, page 536
19.4.2, Semiconductor Junctions, page 537
19.4.3, Boltzmann Equation for Semiconductors, page 540
19.4.4, Detailed Theory of Rectification, page 542
19.4.5, Transistor, page 545
19.5, Inversion Layers, page 548
19.5.1, Heterostructures, page 548
19.5.2, Quantum Point Contact, page 550
19.5.3, Quantum Dot, page 553
Problems, page 556
References, page 557
PART V: OPTICAL PROPERTIES
Chapter 20: Phenomenological Theory, page 561
20.1, Introduction, page 561
20.2, Maxwell's Equations, page 563
20.2.1, Traveling Waves, page 565
20.2.2, Mechanical Oscillators as Dielectric Function, page 566
20.3, Kramers--Kronig Relations, page 568
20.3.1, Application to Optical Experiments, page 570
20.4, The Kubo--Greenwood Formula, page 573
20.4.1, Born Approximation, page 573
20.4.2, Susceptibility, page 577
20.4.3, Many-Body Green Functions, page 578
Problems, page 578
References, page 581
Chapter 21: Optical Properties of Semiconductors, page 583
21.1, Introduction, page 583
21.2, Cyclotron Resonance, page 583
21.2.1, Electron Energy Surfaces, page 586
21.3, Semiconductor Band Gaps, page 588
21.3.1, Direct Transitions, page 588
21.3.2, Indirect Transitions, page 589
21.4, Excitons, page 591
21.4.1, Mott--Wannier Excitons, page 591
21.4.2, Frenkel Excitons, page 594
21.4.3, Electron--Hole Liquid, page 595
21.5, Optoelectronics, page 595
21.5.1, Solar Cells, page 595
21.5.2, Lasers, page 596
Problems, page 602
References, page 606
Chapter 22: Optical Properties of Insulators, page 609
22.1, Introduction, page 609
22.2, Polarization, page 609
22.2.1, Ferroelectrics, page 609
22.2.2, Clausius--Mossotti Relation, page 611
22.3, Optical Modes in Ionic Crystals, page 613
22.3.1, Polaritons, page 616
22.3.2, Polarons, page 618
22.3.3, Experimental Observations of Polarons, page 623
22.4, Point Defects and Color Centers, page 623
22.4.1, Vacancies, page 624
22.4.2, F Centers, page 625
22.4.3, Electron Spin Resonance and Electron Nuclear Double Resonance, page 626
22.4.4, Other Centers, page 628
22.4.5, Franck--Condon Effect, page 628
22.4.6, Urbach Tails, page 632
Problems, page 633
References, page 635
Chapter 23: Optical Properties of Metals and Inelastic Scattering , page 637
23.1, Introduction, page 637
23.1.1, Plasma Frequency, page 637
23.2, Metals at Low Frequencies, page 640
23.2.1, Anomalous Skin Effect, page 642
23.3, Plasmons, page 643
23.3.1, Experimental Observation of Plasmons, page 644
23.4, Interband Transitions, page 646
23.5, Brillouin and Raman Scattering, page 649
23.5.1, Brillouin Scattering, page 650
23.5.2, Raman Scattering, page 651
23.5.3, Inelastic X-Ray Scattering, page 651
23.6, Photoemission, page 651
23.6.1, Measurement of Work Functions, page 651
23.6.2, Angle-Resolved Photoemission, page 654
23.6.3, Core-Level Photoemission and Charge-Transfer Insulators, page 658
Problems, page 664
References, page 667
PART VI: MAGNETISM
Chapter 24: Classical Theories of Magnetism and Ordering, page 671
24.1, Introduction, page 671
24.2, Three Views of Magnetism, page 671
24.2.1, From Magnetic Moments, page 671
24.2.2, From Conductivity, page 672
24.2.3, From a Free Energy, page 673
24.3, Magnetic Dipole Moments, page 675
24.3.1, Spontaneous Magnetization of Ferromagnets, page 678
24.3.2, Ferrimagnets, page 679
24.3.3, Antiferromagnets, page 681
24.4, Mean Field Theory and the Ising Model, page 682
24.4.1, Domains , page 684
24.4.2, Hysteresis, page 687
24.5, Other Order--Disorder Transitions, page 688
24.5.1, Alloy Superlattices, page 688
24.5.2, Spin Glasses, page 691
24.6, Critical Phenomena, page 691
24.6.1, Landau Free Energy, page 692
24.6.2, Scaling Theory, page 698
Problems, page 702
References, page 705
Chapter 25: Magnetism of Ions and Electrons, page 707
25.1, Introduction, page 707
25.2, Atomic Magnetism, page 709
25.2.1, Hund's Rules, page 710
25.2.2, Curie's Law, page 714
25.3, Magnetism of the Free-Electron Gas, page 717
25.3.1, Pauli Paramagnetism, page 718
25.3.2, Landau Diamagnetism, page 719
25.3.3, Aharonov--Bohm Effect, page 722
25.4, Tightly Bound Electrons in Magnetic Fields, page 724
25.5, Quantum Hall Effect, page 728
25.5.1, Integer Quantum Hall Effect, page 728
25.5.2, Fractional Quantum Hall Effect, page 733
Problems, page 739
References, page 742
Michael Marder
Center for Nonlinear Dynamics, University of Texas, Austin
TABLE OF CONTENTS
PART I: ATOMIC STRUCTURE
Chapter 1: The Idea of Crystals, page 3
1.1, Introduction, page 3
1.1.1, Why are Solids Crystalline?, page 4
1.2, Two-Dimensional Lattices, page 6
1.2.1, Bravais Lattices, page 6
1.2.2, Enumeration of Two-Dimensional Bravais Lattices, page 7
1.2.3, Lattices with Bases, page 7
1.2.4, Primitive Cells, page 9
1.2.5, Wigner--Seitz Cells, page 10
1.3, Symmetries, page 11
1.3.1, The Space Group, page 11
1.3.2, Translation and Point Groups, page 11
Problems, page 13
References, page 15
Chapter 2: Three-Dimensional Lattice, page 17
2.1, Introduction, page 17
2.1.1, Distribution Among Elements, page 17
2.2, Monatomic Lattices, page 20
2.2.1, The Simple Cubic Lattice, page 20
2.2.2, The Face-Centered Cubic Lattice, page 20
2.2.3, The Body-Centered Cubic Lattice, page 21
2.2.4, The Hexagonal Lattice, page 22
2.2.5, The Hexagonal Close-Packed Lattice, page 23
2.2.6, The Diamond Lattice, page 24
2.3, Compounds , page 24
2.3.1, Rocksalt---Sodium Chloride, page 25
2.3.2, Cesium Chloride, page 26
2.3.3, Fluorite---Calcium Fluoride, page 26
2.3.4, Zincblende---Zinc Sulfide, page 26
2.3.5, Wurtzite---Zinc Oxide, page 28
2.3.6, Perovskite---Calcium Titanate , page 28
2.4, Classification of Lattices by Symmetry, page 28
2.4.1, Fourteen Bravais Lattices and Seven Crystal Systems, page 30
2.5, Symmetries of Lattices with Bases, page 32
2.5.1, Thirty-Two Crystallographic Point Groups, page 32
2.5.2, Two Hundred Thirty Distinct Lattices, page 36
2.6, Some Macroscopic Implications of Microscopic Symmetries, page 37
2.6.1, Pyroelectricity, page 37
2.6.2, Piezoelectricity, page 37
2.6.3, Optical Activity, page 38
Problems, page 38
References, page 41
Chapter 3: Experimental Determination of Crystal Structure, page 43
3.1, Introduction, page 43
3.2, Theory of Scattering from Crystals, page 44
3.2.1, Lattice Sums, page 47
3.2.2, Reciprocal Lattice, page 48
3.2.3, Miller Indices, page 51
3.2.4, Scattering from a Lattice with a Basis, page 52
3.3, Experimental Methods, page 54
3.3.1, Laue Method, page 55
3.3.2, Rotating Crystal Method, page 56
3.3.3, Powder Method, page 58
3.4, Further Features of Scattering Experiments, page 59
3.4.1, Interaction of X-Rays with Matter, page 60
3.4.2, Production of X-Rays, page 60
3.4.3, Neutrons, page 61
3.4.4, Electrons, page 61
3.4.5, Deciphering Complex Structures, page 63
3.4.6, Accuracy of Structure Determinations, page 64
Problems, page 65
References, page 67
Chapter 4: Surfaces and Interface, page 69
4.1, Introduction, page 69
4.2, Geometry of Interfaces, page 69
4.2.1, Coherent and Commensurate Interfaces, page 70
4.2.2, Stacking Period and Interplanar Spacing, page 71
4.2.3, Other Topics in Surface Structure, page 73
4.3, Experimental Observation and Creation of Surfaces, page 73
4.3.1, Low-Energy Electron Diffraction (LEED), page 74
4.3.2, Reflection High-Energy Electron Diffraction (RHEED), page 75
4.3.3, Molecular Beam Epitaxy (MBE), page 76
4.3.4, Field Ion Microscopy (FIM), page 77
4.3.5, Scanning Tunneling Microscopy (STM), page 77
4.3.6, Atomic Force Microscopy (AFM), page 82
4.3.7, High Resolution Electron Microscopy (HREM), page 82
Problems, page 82
References, page 85
Chapter 5: Complex Structure, page 87
5.1, Introduction, page 87
5.2, Alloys, page 87
5.2.1, Equilibrium Structures, page 87
5.2.2, Phase Diagrams, page 89
5.2.3, Superlattices, page 90
5.2.4, Phase Separation, page 91
5.2.5, Nonequilibrium Structures in Alloys, page 94
5.2.6, Dynamics of Phase Separation, page 95
5.3, Simulations, page 97
5.3.1, Monte Carlo, page 97
5.3.2, Molecular Dynamics, page 98
5.4, Liquids, page 99
5.4.1, Correlation Functions, page 99
5.4.2, Extended X-Ray Absorption Fine Structure (EXAFS), page 101
5.4.3, Calculating Correlation Functions, page 103
5.5, Glasses, page 103
5.6, Liquid Crystals, page 107
5.6.1, Nematics, Cholesterics, and Smectics, page 108
5.6.2, Liquid Crystal Order Parameter, page 109
5.7, Polymers, page 110
5.7.1, Ideal Radius of Gyration, page 111
5.8, Quasicrystals, page 115
5.8.1, One-Dimensional Quasicrystal, page 116
5.8.2, Two-Dimensional Quasicrystals---Penrose Tiles, page 121
5.8.3, Experimental Observations, page 124
5.8.4, Fullerenes, page 124
Problems, page 125
References, page 129
PART II: ELECTRONIC STRUCTURE
Chapter 6: The Single-Electron Model, page 135
6.1, Introduction, page 135
6.2, The Basic Hamiltonian, page 137
6.3, Densities of States, page 139
6.3.1, Definition of Density of States ${D, page {140}
6.3.2, Results for Free Electrons, page 141
6.4, Statistical Mechanics of Noninteracting Electrons, page 143
6.5, Sommerfeld Expansion, page 146
6.5.1, Specific Heat of Noninteracting Electrons at Low Temperatures , page 149
Problems, page 150
References, page 153
Chapter 7: The Schroedinger Equation and Symmetry, page 155
7.1, Introduction, page 155
7.2, Translational Symmetry---Bloch's Theorem, page 155
7.2.1, Van Hove Singularities, page 160
7.2.2, Fourier Analysis of Bloch's Theorem, page 163
7.2.3, Kronig--Penney Model, page 166
7.3, Rotational Symmetry---Group Representations, page 169
7.3.1, Classes and Characters, page 175
7.3.2, Consequences of point group symmetries for Schr\"odinger's equation, page 178
Problems, page 181
References, page 184
Chapter 8: Nearly Free and Tightly Bound Electrons, page 185
8.1, Introduction, page 185
8.2, Nearly Free Electrons, page 185
8.2.1, Degenerate Perturbation Theory, page 187
8.3, Brillouin Zones, page 189
8.3.1, Nearly Free Electron Fermi Surfaces, page 191
8.4, Tightly Bound Electrons, page 194
8.4.1, Wannier Functions, page 194
8.4.2, Tight Binding Model, page 197
Problems, page 199
References, page 202
Chapter 9: Electron--Electron Interactions, page 203
9.1, Introduction, page 203
9.2, Hartree and Hartree--Fock Equations, page 204
9.2.1, Variational Principle, page 205
9.2.2, Hartree--Fock Equations, page 205
9.2.3, Numerical Implementation, page 209
9.2.4, Hartree--Fock Equations for Jellium, page 212
9.3, Density Functional Theory, page 214
9.3.1, Thomas--Fermi Theory, page 216
9.3.2, Kohn--Sham Equations, page 218
9.4, Stability of Matter, page 220
Problems, page 223
References, page 226
Chapter 10: Calculation of Band Structures, page 229
10.1, Introduction, page 229
10.2, Numerical Methods, page 230
10.2.1, Pseudopotentials and Orthogonalized Planes Waves (OPW), page 230
10.2.2, Linear Combination of Atomic Orbitals (LCAO), page 235
10.2.3, Plane Waves, page 237
10.2.4, Linear Augmented Plane Waves (LAPW), page 240
10.2.5, Linearized Muffin Tin Orbitals (LMTO), page 243
10.3, Definition of Metals, Insulators, and Semiconductors, page 246
10.4, Brief Survey of the Periodic Table, page 248
10.4.1, Noble Gases, page 248
10.4.2, Nearly Free Electron Metals, page 250
10.4.3, Semiconductors, page 252
10.4.4, Transition Metals, page 252
10.4.5, Rare Earths, page 252
Problems, page 254
References, page 258
PART III: MECHANICAL PROPERTIES
Chapter 11: Cohesion of Solids, page 263
11.1, Introduction, page 263
11.1.1, Radii of Atoms, page 263
11.2, Noble Gases, page 265
11.3, Ionic Crystals, page 269
11.3.1, Ewald Sums, page 270
11.4, Metals, page 272
11.4.1, Use of Pseudopotentials, page 275
11.5, Band Structure Energy, page 276
11.5.1, Peierls Distortion, page 277
11.5.2, Structural Phase Transitions, page 279
11.6, Hydrogen-Bonded Solids, page 280
11.7, Cohesive Energy from Band Calculations, page 280
11.8, Classical Potentials, page 282
Problems, page 283
References, page 285
Chapter 12: Elasticity, page 287
12.1, Introduction, page 287
12.2, General Theory of Linear Elasticity , page 287
12.2.1, Solids of Cubic Symmetry, page 289
12.2.2, Isotropic Solids, page 290
12.3, Other Constitutive Laws, page 295
12.3.1, Liquid Crystals, page 295
12.3.2, Rubber, page 298
12.3.3, Composite and Granular Materials, page 301
Problems, page 301
References, page 303
Chapter 13: Phonons , page 305
13.1, Introduction, page 305
13.2, Vibrations of a Classical Lattice, page 305
13.2.1, Normal Modes, page 307
13.2.2, Lattice with a Basis, page 309
13.3, Vibrations of a Quantum--Mechanical Lattice, page 313
13.3.1, Phonon Specific Heat, page 317
13.3.2, Einstein and Debye Models, page 321
13.3.3, Thermal Expansion, page 324
13.4, Inelastic Scattering from Phonons, page 326
13.4.1, Neutron Scattering, page 327
13.4.2, Formal Theory of Neutron Scattering, page 329
13.4.3, Averaging Exponentials, page 333
13.4.4, Evaluation of Structure Factor, page 335
13.4.5, Kohn Anomalies, page 336
13.5, The M\"ossbauer Effect, page 336
Problems, page 339
References, page 340
Chapter 14: Dislocations and Cracks, page 343
14.1, Introduction, page 343
14.2, Dislocations, page 345
14.2.1, Experimental Observations of Dislocations, page 347
14.2.2, Force to Move a Dislocation, page 350
14.2.3, One-Dimensional Dislocations: Frenkel--Kontorova Model, page 350
14.3, Two-Dimensional Dislocations and Hexatic Phases, page 353
14.3.1, Impossibility of Crystalline Order in Two Dimensions, page 353
14.3.2, Orientational Order, page 355
14.3.3, Kosterlitz--Thouless--Berezinskii Transition, page 356
14.4, Cracks, page 363
14.4.1, Fracture of a Strip, page 363
14.4.2, Stresses Around an Elliptical Hole, page 366
14.4.3, Stress Intensity Factor, page 368
14.4.4, Atomic Aspects of Fracture, page 368
Problems, page 370
References, page 373
Chapter 15: Fluid Mechanics, page 375
15.1, Introduction, page 375
15.2, Newtonian Fluids, page 375
15.2.1, Euler's Equation, page 375
15.2.2, Navier--Stokes Equation, page 377
15.3, Polymeric Solutions, page 378
15.4, Plasticity, page 385
15.5, Superfluid $^4$He, page 389
15.5.1, Two-Fluid Hydrodynamics, page 392
15.5.2, Second Sound, page 393
15.5.3, Origin of Superfluidity, page 395
15.5.4, Lagrangian Theory of Wave Function, page 400
15.5.5, Superfluid 3He, page 403
Problems, page 404
References, page 408
PART IV: ELECTRON TRANSPORT
Chapter 16: Dynamics of Bloch Electrons, page 413
16.1, Introduction, page 413
16.1.1, Drude Model, page 413
16.2, Semiclassical Electron Dynamics, page 415
16.2.1, Bloch Oscillations, page 416
16.2.2, k . P Method, page 417
16.2.3, Effective Mass, page 419
16.3, Noninteracting Electrons in an Electric Field, page 419
16.3.1, Zener Tunneling, page 422
16.4, Semiclassical Equations from Wave Packets, page 425
16.4.1, Formal Dynamics of Wave Packets, page 425
16.5, Quantizing Semiclassical Dynamics, page 430
16.5.1, Wannier--Stark Ladders, page 432
16.5.2, de Haas--van Alphen Effect, page 432
16.5.3, Experimental Measurements of Fermi Surfaces, page 434
Problems, page 437
References, page 440
Chapter 17: Transport Phenomena and Fermi Liquid Theory, page 443
17.1, Introduction, page 443
17.2, Boltzmann Equation, page 443
17.2.1, Boltzmann Equation, page 445
17.2.2, Relaxation Time Approximation, page 446
17.2.3, Relation to Rate of Production of Entropy, page 448
17.3, Transport Symmetries, page 449
17.3.1, Onsager Relations, page 450
17.4, Thermoelectric Phenomena, page 451
17.4.1, Electrical Current, page 451
17.4.2, Effective Mass and Holes, page 453
17.4.3, Mixed Thermal and Electrical Gradients, page 454
17.4.4, Wiedemann--Franz Law, page 455
17.4.5, Thermopower---Seebeck Effect, page 456
17.4.6, Peltier Effect, page 457
17.4.7, Thomson Effect, page 457
17.4.8, Hall Effect, page 459
17.4.9, Magnetoresistance, page 461
17.4.10, Giant Magnetoresistance, page 462
17.5, Fermi Liquid Theory, page 462
17.5.1, Basic Ideas, page 462
17.5.2, Statistical Mechanics of Quasi-Particles, page 464
17.5.3, Effective Mass, page 466
17.5.4, Specific Heat, page 468
17.5.5, Fermi Liquid Parameters, page 469
17.5.6, Traveling Waves, page 470
17.5.7, Comparison with Experiment in 3He, page 473
Problems, page 474
References, page 478
Chapter 18: Microscopic Theories of Conduction, page 481
18.1, Introduction, page 481
18.2, Weak Scattering Theory of Conductivity, page 481
18.2.1, General Formula for Relaxation Time, page 481
18.2.2, Matthiessen's Rule, page 486
18.2.3, Fluctuations, page 487
18.3, Metal--Insulator Transitions, page 488
18.3.1, Types of Impurities, page 488
18.3.2, Impurity Scattering and Green's Functions , page 492
18.3.3, Green's Functions, page 493
18.3.4, Single Impurity, page 497
18.4, Coherent Potential Approximation, page 499
18.5, Localization, page 500
18.5.1, Exact Results in One Dimension, page 501
18.5.2, Scaling Theory of Localization, page 505
18.5.3, Comparison with Experiment, page 509
Problems, page 510
References, page 514
Chapter 19: Electronics, page 517
19.1, Introduction, page 517
19.2, Metal Interfaces, page 518
19.2.1, Work Functions, page 519
19.2.2, Schottky Barrier, page 520
19.2.3, Contact Potentials, page 522
19.3, Semiconductors, page 524
19.3.1, Pure Semiconductors, page 525
19.3.2, Semiconductor in Equilibrium, page 528
19.3.3, Intrinsic Semiconductor, page 530
19.3.4, Extrinsic Semiconductor, page 531
19.4, Diodes and Transistors, page 533
19.4.1, Surface States, page 536
19.4.2, Semiconductor Junctions, page 537
19.4.3, Boltzmann Equation for Semiconductors, page 540
19.4.4, Detailed Theory of Rectification, page 542
19.4.5, Transistor, page 545
19.5, Inversion Layers, page 548
19.5.1, Heterostructures, page 548
19.5.2, Quantum Point Contact, page 550
19.5.3, Quantum Dot, page 553
Problems, page 556
References, page 557
PART V: OPTICAL PROPERTIES
Chapter 20: Phenomenological Theory, page 561
20.1, Introduction, page 561
20.2, Maxwell's Equations, page 563
20.2.1, Traveling Waves, page 565
20.2.2, Mechanical Oscillators as Dielectric Function, page 566
20.3, Kramers--Kronig Relations, page 568
20.3.1, Application to Optical Experiments, page 570
20.4, The Kubo--Greenwood Formula, page 573
20.4.1, Born Approximation, page 573
20.4.2, Susceptibility, page 577
20.4.3, Many-Body Green Functions, page 578
Problems, page 578
References, page 581
Chapter 21: Optical Properties of Semiconductors, page 583
21.1, Introduction, page 583
21.2, Cyclotron Resonance, page 583
21.2.1, Electron Energy Surfaces, page 586
21.3, Semiconductor Band Gaps, page 588
21.3.1, Direct Transitions, page 588
21.3.2, Indirect Transitions, page 589
21.4, Excitons, page 591
21.4.1, Mott--Wannier Excitons, page 591
21.4.2, Frenkel Excitons, page 594
21.4.3, Electron--Hole Liquid, page 595
21.5, Optoelectronics, page 595
21.5.1, Solar Cells, page 595
21.5.2, Lasers, page 596
Problems, page 602
References, page 606
Chapter 22: Optical Properties of Insulators, page 609
22.1, Introduction, page 609
22.2, Polarization, page 609
22.2.1, Ferroelectrics, page 609
22.2.2, Clausius--Mossotti Relation, page 611
22.3, Optical Modes in Ionic Crystals, page 613
22.3.1, Polaritons, page 616
22.3.2, Polarons, page 618
22.3.3, Experimental Observations of Polarons, page 623
22.4, Point Defects and Color Centers, page 623
22.4.1, Vacancies, page 624
22.4.2, F Centers, page 625
22.4.3, Electron Spin Resonance and Electron Nuclear Double Resonance, page 626
22.4.4, Other Centers, page 628
22.4.5, Franck--Condon Effect, page 628
22.4.6, Urbach Tails, page 632
Problems, page 633
References, page 635
Chapter 23: Optical Properties of Metals and Inelastic Scattering , page 637
23.1, Introduction, page 637
23.1.1, Plasma Frequency, page 637
23.2, Metals at Low Frequencies, page 640
23.2.1, Anomalous Skin Effect, page 642
23.3, Plasmons, page 643
23.3.1, Experimental Observation of Plasmons, page 644
23.4, Interband Transitions, page 646
23.5, Brillouin and Raman Scattering, page 649
23.5.1, Brillouin Scattering, page 650
23.5.2, Raman Scattering, page 651
23.5.3, Inelastic X-Ray Scattering, page 651
23.6, Photoemission, page 651
23.6.1, Measurement of Work Functions, page 651
23.6.2, Angle-Resolved Photoemission, page 654
23.6.3, Core-Level Photoemission and Charge-Transfer Insulators, page 658
Problems, page 664
References, page 667
PART VI: MAGNETISM
Chapter 24: Classical Theories of Magnetism and Ordering, page 671
24.1, Introduction, page 671
24.2, Three Views of Magnetism, page 671
24.2.1, From Magnetic Moments, page 671
24.2.2, From Conductivity, page 672
24.2.3, From a Free Energy, page 673
24.3, Magnetic Dipole Moments, page 675
24.3.1, Spontaneous Magnetization of Ferromagnets, page 678
24.3.2, Ferrimagnets, page 679
24.3.3, Antiferromagnets, page 681
24.4, Mean Field Theory and the Ising Model, page 682
24.4.1, Domains , page 684
24.4.2, Hysteresis, page 687
24.5, Other Order--Disorder Transitions, page 688
24.5.1, Alloy Superlattices, page 688
24.5.2, Spin Glasses, page 691
24.6, Critical Phenomena, page 691
24.6.1, Landau Free Energy, page 692
24.6.2, Scaling Theory, page 698
Problems, page 702
References, page 705
Chapter 25: Magnetism of Ions and Electrons, page 707
25.1, Introduction, page 707
25.2, Atomic Magnetism, page 709
25.2.1, Hund's Rules, page 710
25.2.2, Curie's Law, page 714
25.3, Magnetism of the Free-Electron Gas, page 717
25.3.1, Pauli Paramagnetism, page 718
25.3.2, Landau Diamagnetism, page 719
25.3.3, Aharonov--Bohm Effect, page 722
25.4, Tightly Bound Electrons in Magnetic Fields, page 724
25.5, Quantum Hall Effect, page 728
25.5.1, Integer Quantum Hall Effect, page 728
25.5.2, Fractional Quantum Hall Effect, page 733
Problems, page 739
References, page 742