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Özet
Özet
A modern, unified treatment of condensed matter physics
This new work presents for the first time in decades a sweeping review of the whole field of condensed matter physics. It consolidates new and classic topics from disparate sources, teaching "not only about the effective masses of electrons in semiconductor crystals and band theory, but also about quasicrystals, dynamics of phase separation, why rubber is more floppy than steel, electron interference in nanometer-sized channels, and the quantum Hall effect."
Six major areas are covered---atomic structure, electronic structure, mechanical properties, electron transport, optical properties, and magnetism. But rather than defining the field in terms of particular materials, the author focuses on the way condensed matter physicists approach physical problems, combining phenomenology and microscopic arguments with information from experiments. For graduate students and professionals, researchers and engineers, applied mathematicians and materials scientists, Condensed Matter Physics provides:
* An exciting collection of new topics from the past two decades.
* A thorough treatment of classic topics, including band theory, transport theory, and semiconductor physics.
* Over 300 figures, incorporating many images from experiments.
* Frequent comparison of theory and experiment, both when they agree and when problems are still unsolved.
* More than 50 tables of data and a detailed index.
* Ample end-of-chapter problems, including computational exercises.
* Over 1000 references, both recent and historically significant.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Author Notes
Michael P. Marder, Ph.D., is Associate Professor of Physics at the University of Texas at Austin and a member of the internationally known Center for Nonlinear Dynamics.
Table of Contents
| Preface | p. xix |
| References | p. xxii |
| I Atomic Structure | p. 1 |
| 1 The Idea of Crystals | p. 3 |
| 1.1 Introduction | p. 3 |
| 1.1.1 Why are Solids Crystalline? | p. 4 |
| 1.2 Two-Dimensional Lattices | p. 6 |
| 1.2.1 Bravais Lattices | p. 6 |
| 1.2.2 Enumeration of Two-Dimensional Bravais Lattices | p. 7 |
| 1.2.3 Lattices with Bases | p. 7 |
| 1.2.4 Primitive Cells | p. 9 |
| 1.2.5 Wigner-Seitz Cells | p. 10 |
| 1.3 Symmetries | p. 11 |
| 1.3.1 The Space Group | p. 11 |
| 1.3.2 Translation and Point Groups | p. 11 |
| Problems | p. 13 |
| References | p. 15 |
| 2 Three-Dimensional Lattices | p. 17 |
| 2.1 Introduction | p. 17 |
| 2.1.1 Distribution Among Elements | p. 17 |
| 2.2 Monatomic Lattices | p. 20 |
| 2.2.1 The Simple Cubic Lattice | p. 20 |
| 2.2.2 The Face-Centered Cubic Lattice | p. 20 |
| 2.2.3 The Body-Centered Cubic Lattice | p. 21 |
| 2.2.4 The Hexagonal Lattice | p. 22 |
| 2.2.5 The Hexagonal Close-Packed Lattice | p. 23 |
| 2.2.6 The Diamond Lattice | p. 24 |
| 2.3 Compounds | p. 24 |
| 2.3.1 Rocksalt--Sodium Chloride | p. 25 |
| 2.3.2 Cesium Chloride | p. 26 |
| 2.3.3 Fluorite--Calcium Fluoride | p. 26 |
| 2.3.4 Zincblende--Zinc Sulfide | p. 26 |
| 2.3.5 Wurtzite--Zinc Oxide | p. 28 |
| 2.3.6 Perovskite--Calcium Titanate | p. 28 |
| 2.4 Classification of Lattices by Symmetry | p. 28 |
| 2.4.1 Fourteen Bravais Lattices and Seven Crystal Systems | p. 30 |
| 2.5 Symmetries of Lattices with Bases | p. 32 |
| 2.5.1 Thirty-Two Crystallographic Point Groups | p. 32 |
| 2.5.2 Two Hundred Thirty Distinct Lattices | p. 36 |
| 2.6 Some Macroscopic Implications of Microscopic Symmetries | p. 37 |
| 2.6.1 Pyroelectricity | p. 37 |
| 2.6.2 Piezoelectricity | p. 37 |
| 2.6.3 Optical Activity | p. 38 |
| Problems | p. 38 |
| References | p. 41 |
| 3 Experimental Determination of Crystal Structures | p. 43 |
| 3.1 Introduction | p. 43 |
| 3.2 Theory of Scattering from Crystals | p. 44 |
| 3.2.1 Lattice Sums | p. 47 |
| 3.2.2 Reciprocal Lattice | p. 48 |
| 3.2.3 Miller Indices | p. 51 |
| 3.2.4 Scattering from a Lattice with a Basis | p. 52 |
| 3.3 Experimental Methods | p. 54 |
| 3.3.1 Laue Method | p. 55 |
| 3.3.2 Rotating Crystal Method | p. 56 |
| 3.3.3 Powder Method | p. 58 |
| 3.4 Further Features of Scattering Experiments | p. 59 |
| 3.4.1 Interaction of X-Rays with Matter | p. 60 |
| 3.4.2 Production of X-Rays | p. 60 |
| 3.4.3 Neutrons | p. 61 |
| 3.4.4 Electrons | p. 61 |
| 3.4.5 Deciphering Complex Structures | p. 63 |
| 3.4.6 Accuracy of Structure Determinations | p. 64 |
| Problems | p. 65 |
| References | p. 67 |
| 4 Surfaces and Interfaces | p. 69 |
| 4.1 Introduction | p. 69 |
| 4.2 Geometry of Interfaces | p. 69 |
| 4.2.1 Coherent and Commensurate Interfaces | p. 70 |
| 4.2.2 Stacking Period and Interplanar Spacing | p. 71 |
| 4.2.3 Other Topics in Surface Structure | p. 73 |
| 4.3 Experimental Observation and Creation of Surfaces | p. 73 |
| 4.3.1 Low-Energy Electron Diffraction (LEED) | p. 74 |
| 4.3.2 Reflection High-Energy Electron Diffraction (RHEED) | p. 75 |
| 4.3.3 Molecular Beam Epitaxy (MBE) | p. 76 |
| 4.3.4 Field Ion Microscopy (FIM) | p. 77 |
| 4.3.5 Scanning Tunneling Microscopy (STM) | p. 77 |
| 4.3.6 Atomic Force Microscopy (AFM) | p. 82 |
| 4.3.7 High Resolution Electron Microscopy (HREM) | p. 82 |
| Problems | p. 82 |
| References | p. 85 |
| 5 Complex Structures | p. 87 |
| 5.1 Introduction | p. 87 |
| 5.2 Alloys | p. 87 |
| 5.2.1 Equilibrium Structures | p. 87 |
| 5.2.2 Phase Diagrams | p. 89 |
| 5.2.3 Superlattices | p. 90 |
| 5.2.4 Phase Separation | p. 91 |
| 5.2.5 Nonequilibrium Structures in Alloys | p. 94 |
| 5.2.6 Dynamics of Phase Separation | p. 95 |
| 5.3 Simulations | p. 97 |
| 5.3.1 Monte Carlo | p. 97 |
| 5.3.2 Molecular Dynamics | p. 98 |
| 5.4 Liquids | p. 99 |
| 5.4.1 Correlation Functions | p. 99 |
| 5.4.2 Extended X-Ray Absorption Fine Structure (EXAFS) | p. 101 |
| 5.4.3 Calculating Correlation Functions | p. 103 |
| 5.5 Glasses | p. 103 |
| 5.6 Liquid Crystals | p. 107 |
| 5.6.1 Nematics, Cholesterics, and Smectics | p. 108 |
| 5.6.2 Liquid Crystal Order Parameter | p. 109 |
| 5.7 Polymers | p. 110 |
| 5.7.1 Ideal Radius of Gyration | p. 111 |
| 5.8 Quasicrystals | p. 115 |
| 5.8.1 One-Dimensional Quasicrystal | p. 116 |
| 5.8.2 Two-Dimensional Quasicrystals--Penrose Tiles | p. 121 |
| 5.8.3 Experimental Observations | p. 124 |
| 5.8.4 Fullerenes | p. 124 |
| Problems | p. 125 |
| References | p. 129 |
| II Electronic Structure | p. 133 |
| 6 The Single-Electron Model | p. 135 |
| 6.1 Introduction | p. 135 |
| 6.2 The Basic Hamiltonian | p. 137 |
| 6.3 Densities of States | p. 139 |
| 6.3.1 Definition of Density of States D | p. 140 |
| 6.3.2 Results for Free Electrons | p. 141 |
| 6.4 Statistical Mechanics of Noninteracting Electrons | p. 143 |
| 6.5 Sommerfeld Expansion | p. 146 |
| 6.5.1 Specific Heat of Noninteracting Electrons at Low Temperatures | p. 149 |
| Problems | p. 150 |
| References | p. 153 |
| 7 The Schrodinger Equation and Symmetry | p. 155 |
| 7.1 Introduction | p. 155 |
| 7.2 Translational Symmetry--Bloch's Theorem | p. 155 |
| 7.2.1 Van Hove Singularities | p. 160 |
| 7.2.2 Fourier Analysis of Bloch's Theorem | p. 163 |
| 7.2.3 Kronig-Penney Model | p. 166 |
| 7.3 Rotational Symmetry--Group Representations | p. 169 |
| 7.3.1 Classes and Characters | p. 175 |
| 7.3.2 Consequences of point group symmetries for Schrodinger's equation | p. 178 |
| Problems | p. 181 |
| References | p. 184 |
| 8 Nearly Free and Tightly Bound Electrons | p. 185 |
| 8.1 Introduction | p. 185 |
| 8.2 Nearly Free Electrons | p. 185 |
| 8.2.1 Degenerate Perturbation Theory | p. 187 |
| 8.3 Brillouin Zones | p. 189 |
| 8.3.1 Nearly Free Electron Fermi Surfaces | p. 191 |
| 8.4 Tightly Bound Electrons | p. 194 |
| 8.4.1 Wannier Functions | p. 194 |
| 8.4.2 Tight Binding Model | p. 197 |
| Problems | p. 199 |
| References | p. 202 |
| 9 Electron-Electron Interaction | p. 203 |
| 9.1 Introduction | p. 203 |
| 9.2 Hartree and Hartree-Fock Equations | p. 204 |
| 9.2.1 Variational Principle | p. 205 |
| 9.2.2 Hartree-Fock Equations | p. 205 |
| 9.2.3 Numerical Implementation | p. 209 |
| 9.2.4 Hartree-Fock Equations for Jellium | p. 212 |
| 9.3 Density Functional Theory | p. 214 |
| 9.3.1 Thomas-Fermi Theory | p. 216 |
| 9.3.2 Kohn-Sham Equations | p. 218 |
| 9.4 Stability of Matter | p. 220 |
| Problems | p. 223 |
| References | p. 226 |
| 10 Calculation of Band Structures | p. 229 |
| 10.1 Introduction | p. 229 |
| 10.2 Numerical Methods | p. 230 |
| 10.2.1 Pseudopotentials and Orthogonalized Planes Waves (OPW) | p. 230 |
| 10.2.2 Linear Combination of Atomic Orbitals (LCAO) | p. 235 |
| 10.2.3 Plane Waves | p. 237 |
| 10.2.4 Linear Augmented Plane Waves (LAPW) | p. 240 |
| 10.2.5 Linearized Muffin Tin Orbitals (LMTO) | p. 243 |
| 10.3 Definition of Metals, Insulators, and Semiconductors | p. 246 |
| 10.4 Brief Survey of the Periodic Table | p. 248 |
| 10.4.1 Noble Gases | p. 248 |
| 10.4.2 Nearly Free Electron Metals | p. 250 |
| 10.4.3 Semiconductors | p. 252 |
| 10.4.4 Transition Metals | p. 252 |
| 10.4.5 Rare Earths | p. 252 |
| Problems | p. 254 |
| References | p. 258 |
| III Mechanical Properties | p. 261 |
| 11 Cohesion of Solids | p. 263 |
| 11.1 Introduction | p. 263 |
| 11.1.1 Radii of Atoms | p. 263 |
| 11.2 Noble Gases | p. 265 |
| 11.3 Ionic Crystals | p. 269 |
| 11.3.1 Ewald Sums | p. 270 |
| 11.4 Metals | p. 272 |
| 11.4.1 Use of Pseudopotentials | p. 275 |
| 11.5 Band Structure Energy | p. 276 |
| 11.5.1 Peierls Distortion | p. 277 |
| 11.5.2 Structural Phase Transitions | p. 279 |
| 11.6 Hydrogen-Bonded Solids | p. 280 |
| 11.7 Cohesive Energy from Band Calculations | p. 280 |
| 11.8 Classical Potentials | p. 282 |
| Problems | p. 283 |
| References | p. 285 |
| 12 Elasticity | p. 287 |
| 12.1 Introduction | p. 287 |
| 12.2 General Theory of Linear Elasticity | p. 287 |
| 12.2.1 Solids of Cubic Symmetry | p. 289 |
| 12.2.2 Isotropic Solids | p. 290 |
| 12.3 Other Constitutive Laws | p. 295 |
| 12.3.1 Liquid Crystals | p. 295 |
| 12.3.2 Rubber | p. 298 |
| 12.3.3 Composite and Granular Materials | p. 301 |
| Problems | p. 301 |
| References | p. 303 |
| 13 Phonons | p. 305 |
| 13.1 Introduction | p. 305 |
| 13.2 Vibrations of a Classical Lattice | p. 305 |
| 13.2.1 Normal Modes | p. 307 |
| 13.2.2 Lattice with a Basis | p. 309 |
| 13.3 Vibrations of a Quantum-Mechanical Lattice | p. 313 |
| 13.3.1 Phonon Specific Heat | p. 317 |
| 13.3.2 Einstein and Debye Models | p. 321 |
| 13.3.3 Thermal Expansion | p. 324 |
| 13.4 Inelastic Scattering from Phonons | p. 326 |
| 13.4.1 Neutron Scattering | p. 327 |
| 13.4.2 Formal Theory of Neutron Scattering | p. 329 |
| 13.4.3 Averaging Exponentials | p. 333 |
| 13.4.4 Evaluation of Structure Factor | p. 335 |
| 13.4.5 Kohn Anomalies | p. 336 |
| 13.5 The Mossbauer Effect | p. 336 |
| Problems | p. 339 |
| References | p. 340 |
| 14 Dislocations and Cracks | p. 343 |
| 14.1 Introduction | p. 343 |
| 14.2 Dislocations | p. 345 |
| 14.2.1 Experimental Observations of Dislocations | p. 347 |
| 14.2.2 Force to Move a Dislocation | p. 350 |
| 14.2.3 One-Dimensional Dislocations: Frenkel-Kontorova Model | p. 350 |
| 14.3 Two-Dimensional Dislocations and Hexatic Phases | p. 353 |
| 14.3.1 Impossibility of Crystalline Order in Two Dimensions | p. 353 |
| 14.3.2 Orientational Order | p. 355 |
| 14.3.3 Kosterlitz-Thouless-Berezinskii Transition | p. 356 |
| 14.4 Cracks | p. 363 |
| 14.4.1 Fracture of a Strip | p. 363 |
| 14.4.2 Stresses Around an Elliptical Hole | p. 366 |
| 14.4.3 Stress Intensity Factor | p. 368 |
| 14.4.4 Atomic Aspects of Fracture | p. 368 |
| Problems | p. 370 |
| References | p. 373 |
| 15 Fluid Mechanics | p. 375 |
| 15.1 Introduction | p. 375 |
| 15.2 Newtonian Fluids | p. 375 |
| 15.2.1 Euler's Equation | p. 375 |
| 15.2.2 Navier-Stokes Equation | p. 377 |
| 15.3 Polymeric Solutions | p. 378 |
| 15.4 Plasticity | p. 385 |
| 15.5 Superfluid [superscript 4]He | p. 389 |
| 15.5.1 Two-Fluid Hydrodynamics | p. 392 |
| 15.5.2 Second Sound | p. 393 |
| 15.5.3 Origin of Superfluidity | p. 395 |
| 15.5.4 Lagrangian Theory of Wave Function | p. 400 |
| 15.5.5 Superfluid [superscript 3]He | p. 403 |
| Problems | p. 404 |
| References | p. 408 |
| IV Electron Transport | p. 411 |
| 16 Dynamics of Bloch Electrons | p. 413 |
| 16.1 Introduction | p. 413 |
| 16.1.1 Drude Model | p. 413 |
| 16.2 Semiclassical Electron Dynamics | p. 415 |
| 16.2.1 Bloch Oscillations | p. 416 |
| 16.2.2 k.P Method | p. 417 |
| 16.2.3 Effective Mass | p. 419 |
| 16.3 Noninteracting Electrons in an Electric Field | p. 419 |
| 16.3.1 Zener Tunneling | p. 422 |
| 16.4 Semiclassical Equations from Wave Packets | p. 425 |
| 16.4.1 Formal Dynamics of Wave Packets | p. 425 |
| 16.5 Quantizing Semiclassical Dynamics | p. 430 |
| 16.5.1 Wannier-Stark Ladders | p. 432 |
| 16.5.2 de Haas-van Alphen Effect | p. 432 |
| 16.5.3 Experimental Measurements of Fermi Surfaces | p. 434 |
| Problems | p. 437 |
| References | p. 440 |
| 17 Transport Phenomena and Fermi Liquid Theory | p. 443 |
| 17.1 Introduction | p. 443 |
| 17.2 Boltzmann Equation | p. 443 |
| 17.2.1 Boltzmann Equation | p. 445 |
| 17.2.2 Relaxation Time Approximation | p. 446 |
| 17.2.3 Relation to Rate of Production of Entropy | p. 448 |
| 17.3 Transport Symmetries | p. 449 |
| 17.3.1 Onsager Relations | p. 450 |
| 17.4 Thermoelectric Phenomena | p. 451 |
| 17.4.1 Electrical Current | p. 451 |
| 17.4.2 Effective Mass and Holes | p. 453 |
| 17.4.3 Mixed Thermal and Electrical Gradients | p. 454 |
| 17.4.4 Wiedemann-Franz Law | p. 455 |
| 17.4.5 Thermopower--Seebeck Effect | p. 456 |
| 17.4.6 Peltier Effect | p. 457 |
| 17.4.7 Thomson Effect | p. 457 |
| 17.4.8 Hall Effect | p. 459 |
| 17.4.9 Magnetoresistance | p. 461 |
| 17.4.10 Giant Magnetoresistance | p. 462 |
| 17.5 Fermi Liquid Theory | p. 462 |
| 17.5.1 Basic Ideas | p. 462 |
| 17.5.2 Statistical Mechanics of Quasi-Particles | p. 464 |
| 17.5.3 Effective Mass | p. 466 |
| 17.5.4 Specific Heat | p. 468 |
| 17.5.5 Fermi Liquid Parameters | p. 469 |
| 17.5.6 Traveling Waves | p. 470 |
| 17.5.7 Comparison with Experiment in [superscript 3]He | p. 473 |
| Problems | p. 474 |
| References | p. 478 |
| 18 Microscopic Theories of Conduction | p. 481 |
| 18.1 Introduction | p. 481 |
| 18.2 Weak Scattering Theory of Conductivity | p. 481 |
| 18.2.1 General Formula for Relaxation Time | p. 481 |
| 18.2.2 Matthiessen's Rule | p. 486 |
| 18.2.3 Fluctuations | p. 487 |
| 18.3 Metal-Insulator Transitions | p. 488 |
| 18.3.1 Types of Impurities | p. 488 |
| 18.3.2 Impurity Scattering and Green's Functions | p. 492 |
| 18.3.3 Green's Functions | p. 493 |
| 18.3.4 Single Impurity | p. 497 |
| 18.4 Coherent Potential Approximation | p. 499 |
| 18.5 Localization | p. 500 |
| 18.5.1 Exact Results in One Dimension | p. 501 |
| 18.5.2 Scaling Theory of Localization | p. 505 |
| 18.5.3 Comparison with Experiment | p. 509 |
| Problems | p. 510 |
| References | p. 514 |
| 19 Electronics | p. 517 |
| 19.1 Introduction | p. 517 |
| 19.2 Metal Interfaces | p. 518 |
| 19.2.1 Work Functions | p. 519 |
| 19.2.2 Schottky Barrier | p. 520 |
| 19.2.3 Contact Potentials | p. 522 |
| 19.3 Semiconductors | p. 524 |
| 19.3.1 Pure Semiconductors | p. 525 |
| 19.3.2 Semiconductor in Equilibrium | p. 528 |
| 19.3.3 Intrinsic Semiconductor | p. 530 |
| 19.3.4 Extrinsic Semiconductor | p. 531 |
| 19.4 Diodes and Transistors | p. 533 |
| 19.4.1 Surface States | p. 536 |
| 19.4.2 Semiconductor Junctions | p. 537 |
| 19.4.3 Boltzmann Equation for Semiconductors | p. 540 |
| 19.4.4 Detailed Theory of Rectification | p. 542 |
| 19.4.5 Transistor | p. 545 |
| 19.5 Inversion Layers | p. 548 |
| 19.5.1 Heterostructures | p. 548 |
| 19.5.2 Quantum Point Contact | p. 550 |
| 19.5.3 Quantum Dot | p. 553 |
| Problems | p. 556 |
| References | p. 557 |
| V Optical Properties | p. 559 |
| 20 Phenomenological Theory | p. 561 |
| 20.1 Introduction | p. 561 |
| 20.2 Maxwell's Equations | p. 563 |
| 20.2.1 Traveling Waves | p. 565 |
| 20.2.2 Mechanical Oscillators as Dielectric Function | p. 566 |
| 20.3 Kramers-Kronig Relations | p. 568 |
| 20.3.1 Application to Optical Experiments | p. 570 |
| 20.4 The Kubo-Greenwood Formula | p. 573 |
| 20.4.1 Born Approximation | p. 573 |
| 20.4.2 Susceptibility | p. 577 |
| 20.4.3 Many-Body Green Functions | p. 578 |
| Problems | p. 578 |
| References | p. 581 |
| 21 Optical Properties of Semiconductors | p. 583 |
| 21.1 Introduction | p. 583 |
| 21.2 Cyclotron Resonance | p. 583 |
| 21.2.1 Electron Energy Surfaces | p. 586 |
| 21.3 Semiconductor Band Gaps | p. 588 |
| 21.3.1 Direct Transitions | p. 588 |
| 21.3.2 Indirect Transitions | p. 589 |
| 21.4 Excitons | p. 591 |
| 21.4.1 Mott-Wannier Excitons | p. 591 |
| 21.4.2 Frenkel Excitons | p. 594 |
| 21.4.3 Electron-Hole Liquid | p. 595 |
| 21.5 Optoelectronics | p. 595 |
| 21.5.1 Solar Cells | p. 595 |
| 21.5.2 Lasers | p. 596 |
| Problems | p. 602 |
| References | p. 606 |
| 22 Optical Properties of Insulators | p. 609 |
| 22.1 Introduction | p. 609 |
| 22.2 Polarization | p. 609 |
| 22.2.1 Ferroelectrics | p. 609 |
| 22.2.2 Clausius-Mossotti Relation | p. 611 |
| 22.3 Optical Modes in Ionic Crystals | p. 613 |
| 22.3.1 Polaritons | p. 616 |
| 22.3.2 Polarons | p. 618 |
| 22.3.3 Experimental Observations of Polarons | p. 623 |
| 22.4 Point Defects and Color Centers | p. 623 |
| 22.4.1 Vacancies | p. 624 |
| 22.4.2 F Centers | p. 625 |
| 22.4.3 Electron Spin Resonance and Electron Nuclear Double Resonance | p. 626 |
| 22.4.4 Other Centers | p. 628 |
| 22.4.5 Franck-Condon Effect | p. 628 |
| 22.4.6 Urbach Tails | p. 632 |
| Problems | p. 633 |
| References | p. 635 |
| 23 Optical Properties of Metals and Inelastic Scattering | p. 637 |
| 23.1 Introduction | p. 637 |
| 23.1.1 Plasma Frequency | p. 637 |
| 23.2 Metals at Low Frequencies | p. 640 |
| 23.2.1 Anomalous Skin Effect | p. 642 |
| 23.3 Plasmons | p. 643 |
| 23.3.1 Experimental Observation of Plasmons | p. 644 |
| 23.4 Interband Transitions | p. 646 |
| 23.5 Brillouin and Raman Scattering | p. 649 |
| 23.5.1 Brillouin Scattering | p. 650 |
| 23.5.2 Raman Scattering | p. 651 |
| 23.5.3 Inelastic X-Ray Scattering | p. 651 |
| 23.6 Photoemission | p. 651 |
| 23.6.1 Measurement of Work Functions | p. 651 |
| 23.6.2 Angle-Resolved Photoemission | p. 654 |
| 23.6.3 Core-Level Photoemission and Charge-Transfer Insulators | p. 658 |
| Problems | p. 664 |
| References | p. 667 |
| VI Magnetism | p. 669 |
| 24 Classical Theories of Magnetism and Ordering | p. 671 |
| 24.1 Introduction | p. 671 |
| 24.2 Three Views of Magnetism | p. 671 |
| 24.2.1 From Magnetic Moments | p. 671 |
| 24.2.2 From Conductivity | p. 672 |
| 24.2.3 From a Free Energy | p. 673 |
| 24.3 Magnetic Dipole Moments | p. 675 |
| 24.3.1 Spontaneous Magnetization of Ferromagnets | p. 678 |
| 24.3.2 Ferrimagnets | p. 679 |
| 24.3.3 Antiferromagnets | p. 681 |
| 24.4 Mean Field Theory and the Ising Model | p. 682 |
| 24.4.1 Domains | p. 684 |
| 24.4.2 Hysteresis | p. 687 |
| 24.5 Other Order-Disorder Transitions | p. 688 |
| 24.5.1 Alloy Superlattices | p. 688 |
| 24.5.2 Spin Glasses | p. 691 |
| 24.6 Critical Phenomena | p. 691 |
| 24.6.1 Landau Free Energy | p. 692 |
| 24.6.2 Scaling Theory | p. 698 |
| Problems | p. 702 |
| References | p. 705 |
| 25 Magnetism of Ions and Electrons | p. 707 |
| 25.1 Introduction | p. 707 |
| 25.2 Atomic Magnetism | p. 709 |
| 25.2.1 Hund's Rules | p. 710 |
| 25.2.2 Curie's Law | p. 714 |
| 25.3 Magnetism of the Free-Electron Gas | p. 717 |
| 25.3.1 Pauli Paramagnetism | p. 718 |
| 25.3.2 Landau Diamagnetism | p. 719 |
| 25.3.3 Aharonov-Bohm Effect | p. 722 |
| 25.4 Tightly Bound Electrons in Magnetic Fields | p. 724 |
| 25.5 Quantum Hall Effect | p. 728 |
| 25.5.1 Integer Quantum Hall Effect | p. 728 |
| 25.5.2 Fractional Quantum Hall Effect | p. 733 |
| Problems | p. 739 |
| References | p. 742 |
| 26 Quantum Mechanics of Interacting Magnetic Moments | p. 745 |
| 26.1 Introduction | p. 745 |
| 26.2 Origin of Ferromagnetism | p. 745 |
| 26.2.1 Heitler-London Calculation | p. 745 |
| 26.2.2 Spin Hamiltonian | p. 750 |
| 26.3 Heisenberg Model | p. 750 |
| 26.3.1 Indirect Exchange and Superexchange | p. 752 |
| 26.3.2 Ground State | p. 753 |
| 26.3.3 Spin Waves | p. 753 |
| 26.3.4 Spin Waves in Antiferromagnets | p. 756 |
| 26.3.5 Comparison with Experiment | p. 759 |
| 26.4 Ferromagnetism in Transition Metals | p. 759 |
| 26.4.1 Stoner Model | p. 759 |
| 26.4.2 Calculations Within Band Theory | p. 761 |
| 26.5 Kondo Effect | p. 763 |
| 26.5.1 Scaling Theory | p. 768 |
| 26.6 Hubbard Model | p. 772 |
| 26.6.1 Mean-Field Solution | p. 773 |
| Problems | p. 776 |
| References | p. 779 |
| 27 Superconductivity | p. 783 |
| 27.1 Introduction | p. 783 |
| 27.2 Phenomenology of Superconductivity | p. 784 |
| 27.2.1 Phenomenological Free Energy | p. 785 |
| 27.2.2 Thermodynamics of Superconductors | p. 787 |
| 27.2.3 Landau-Ginzburg Free Energy | p. 788 |
| 27.2.4 Type I and Type II Superconductors | p. 789 |
| 27.2.5 Flux Quantization | p. 794 |
| 27.2.6 The Josephson Effect | p. 796 |
| 27.2.7 Circuits with Josephson Junction Elements | p. 798 |
| 27.2.8 SQUIDS | p. 799 |
| 27.2.9 Origin of Josephson's Equations | p. 800 |
| 27.3 Microscopic Theory of Superconductivity | p. 802 |
| 27.3.1 Electron-Ion Interaction | p. 803 |
| 27.3.2 Formal Derivation | p. 806 |
| 27.3.3 Instability of the Normal State: Cooper Problem | p. 808 |
| 27.3.4 Self-Consistent Ground State | p. 812 |
| 27.3.5 Thermodynamics of Superconductors | p. 817 |
| 27.3.6 Superconductor in External Magnetic Field | p. 820 |
| 27.3.7 Derivation of Meissner Effect | p. 824 |
| 27.3.8 Comparison with Experiment | p. 827 |
| 27.3.9 High-Temperature Superconductors | p. 828 |
| Problems | p. 833 |
| References | p. 837 |
| Appendices | p. 841 |
| A Lattice Sums and Fourier Transforms | p. 843 |
| A.1 One-Dimensional Sum | p. 843 |
| A.2 Area Under Peaks | p. 843 |
| A.3 Three-Dimensional Sum | p. 844 |
| A.4 Discrete Case | p. 845 |
| A.5 Convolution | p. 846 |
| A.6 Using the Fast Fourier Transform | p. 846 |
| References | p. 848 |
| B Variational Techniques | p. 849 |
| B.1 Functionals and Functional Derivatives | p. 849 |
| B.2 Time-Independent Schrodinger Equation | p. 850 |
| B.3 Time-Dependent Schrodinger Equation | p. 851 |
| B.4 Method of Steepest Descent | p. 852 |
| References | p. 852 |
| C Second Quantization | p. 853 |
| C.1 Rules | p. 853 |
| C.1.1 States | p. 853 |
| C.1.2 Operators | p. 853 |
| C.1.3 Hamiltonians | p. 854 |
| C.2 Derivations | p. 855 |
| C.2.1 Bosons | p. 855 |
| C.2.2 Fermions | p. 856 |
| Index | p. 859 |
