Condensed matter physics

書誌事項

Condensed matter physics

Michael P. Marder

John Wiley & Sons, c2010

2nd ed

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Now updated-the leading single-volume introduction to solid state and soft condensed matter physics This Second Edition of the unified treatment of condensed matter physics keeps the best of the first, providing a basic foundation in the subject while addressing many recent discoveries. Comprehensive and authoritative, it consolidates the critical advances of the past fifty years, bringing together an exciting collection of new and classic topics, dozens of new figures, and new experimental data. This updated edition offers a thorough treatment of such basic topics as band theory, transport theory, and semiconductor physics, as well as more modern areas such as quasicrystals, dynamics of phase separation, granular materials, quantum dots, Berry phases, the quantum Hall effect, and Luttinger liquids. In addition to careful study of electron dynamics, electronics, and superconductivity, there is much material drawn from soft matter physics, including liquid crystals, polymers, and fluid dynamics. Provides frequent comparison of theory and experiment, both when they agree and when problems are still unsolved Incorporates many new images from experiments Provides end-of-chapter problems including computational exercises Includes more than fifty data tables and a detailed forty-page index Offers a solutions manual for instructors Featuring 370 figures and more than 1,000 recent and historically significant references, this volume serves as a valuable resource for graduate and undergraduate students in physics, physics professionals, engineers, applied mathematicians, materials scientists, and researchers in other fields who want to learn about the quantum and atomic underpinnings of materials science from a modern point of view.

目次

Preface xix References xxii I ATOMIC STRUCTURE 1 1 The Idea of Crystals 3 1.1 Introduction 3 1.1.1 Why are Solids Crystalline? 4 1.2 Two-Dimensional Lattices 6 1.2.1 Bravais Lattices 6 1.2.2 Enumeration of Two-Dimensional Bravais Lattices 7 1.2.3 Lattices with Bases 9 1.2.4 Primitive Cells 9 1.2.5 Wigner-Seitz Cells 10 1.3 Symmetries 11 1.3.1 The Space Group 11 1.3.2 Translation and Point Groups 12 1.3.3 Role of Symmetry 14 Problems 14 References 16 2 Three-Dimensional Lattices 17 2.1 Introduction 17 2.2 Monatomic Lattices 20 2.2.1 The Simple Cubic Lattice 20 2.2.2 The Face-Centered Cubic Lattice 20 2.2.3 The Body-Centered Cubic Lattice 22 2.2.4 The Hexagonal Lattice 23 2.2.5 The Hexagonal Close-Packed Lattice 23 2.2.6 The Diamond Lattice 24 2.3 Compounds 24 2.3.1 Rocksalt-Sodium Chloride 25 2.3.2 Cesium Chloride 26 2.3.3 Fluorite-Calcium Fluoride 26 2.3.4 Zincblende-Zinc Sulfide 27 2.3.5 Wurtzite-Zinc Oxide 28 2.3.6 Perovskite-Calcium Titanate 28 2.4 Classification of Lattices by Symmetry 30 2.4.1 Fourteen Bravais Lattices and Seven Crystal Systems 30 2.5 Symmetries of Lattices with Bases 33 2.5.1 Thirty-Two Crystallographic Point Groups 33 2.5.2 Two Hundred Thirty Distinct Lattices 36 2.6 Some Macroscopic Implications of Microscopic Symmetries 37 2.6.1 Pyroelectricity 37 2.6.2 Piezoelectricity 37 2.6.3 Optical Activity 38 Problems 38 References 41 3 Scattering and Structures 43 3.1 Introduction 43 3.2 Theory of Scattering from Crystals 44 3.2.1 Special Conditions for Scattering 44 3.2.2 Elastic Scattering from Single Atom 46 3.2.3 Wave Scattering from Many Atoms 47 3.2.4 Lattice Sums 48 3.2.5 Reciprocal Lattice 49 3.2.6 Miller Indices 51 3.2.7 Scattering from a Lattice with a Basis 53 3.3 Experimental Methods 54 3.3.1 Laue Method 56 3.3.2 Rotating Crystal Method 57 3.3.3 Powder Method 59 3.4 Further Features of Scattering Experiments 60 3.4.1 Interaction of X-Rays with Matter 60 3.4.2 Production of X-Rays 61 3.4.3 Neutrons 63 3.4.4 Electrons 63 3.4.5 Deciphering Complex Structures 64 3.4.6 Accuracy of Structure Determinations 65 3.5 Correlation Functions 66 3.5.1 Why Bragg Peaks Survive Atomic Motions 66 3.5.2 Extended X-Ray Absorption Fine Structure (EXAFS) 67 3.5.3 Dynamic Light Scattering 68 3.5.4 Application to Dilute Solutions 70 Problems 71 References 73 4 Surfaces and Interfaces 77 4.1 Introduction 77 4.2 Geometry of Interfaces 77 4.2.1 Coherent and Commensurate Interfaces 78 4.2.2 Stacking Period and Interplanar Spacing 79 4.2.3 Other Topics in Surface Structure 81 4.3 Experimental Observation and Creation of Surfaces 82 4.3.1 Low-Energy Electron Diffraction (LEED) 82 4.3.2 Reflection High-Energy Electron Diffraction (RHEED) 84 4.3.3 Molecular Beam Epitaxy (MBE) 84 4.3.4 Field Ion Microscopy (FIM) 85 4.3.5 Scanning Tunneling Microscopy (STM) 86 4.3.6 Atomic Force Microscopy (AFM) 91 4.3.7 High Resolution Electron Microscopy (HREM) 91 Problems 91 References 94 5 Beyond Crystals 97 5.1 Introduction 97 5.2 Diffusion and Random Variables 97 5.2.1 Brownian Motion and the Diffusion Equation 97 5.2.2 Diffusion 98 5.2.3 Derivation from Master Equation 99 5.2.4 Connection Between Diffusion and Random Walks 100 5.3 Alloys 101 5.3.1 Equilibrium Structures 101 5.3.2 Phase Diagrams 102 5.3.3 Superlattices 103 5.3.4 Phase Separation 104 5.3.5 Nonequilibrium Structures in Alloys 106 5.3.6 Dynamics of Phase Separation 108 5.4 Simulations 110 5.4.1 Monte Carlo 110 5.4.2 Molecular Dynamics 112 5.5 Liquids 113 5.5.1 Order Parameters and Long-and Short-Range Order 113 5.5.2 Packing Spheres 114 5.6 Glasses 116 5.7 Liquid Crystals 120 5.7.1 Nematics, Cholesterics, and Smectics 120 5.7.2 Liquid Crystal Order Parameter 122 5.8 Polymers 123 5.8.1 Ideal Radius of Gyration 123 5.9 Colloids and Diffusing-Wave Scattering 128 5.9.1 Colloids 128 5.9.2 Diffusing-Wave Spectroscopy 128 5.10 Quasicrystals 133 5.10.1 One-Dimensional Quasicrystal 134 5.10.2 Two-Dimensional Quasicrystals-Penrose Tiles 139 5.10.3 Experimental Observations 141 5.11 Fullerenes and nanotubes 143 Problems 143 References 149 II ELECTRONIC STRUCTURE 153 6 The Free Fermi Gas and Single Electron Model 155 6.1 Introduction 155 6.2 Starting Hamiltonian 157 6.3 Densities of States 159 6.3.1 Definition of Density of States D 160 6.3.2 Results for Free Electrons 161 6.4 Statistical Mechanics of Noninteracting Electrons 163 6.5 Sommerfeld Expansion 166 6.5.1 Specific Heat of Noninteracting Electrons at Low Temper-atures 169 Problems 171 References 173 7 Non-Interacting Electrons in a Periodic Potential 175 7.1 Introduction 175 7.2 Translational Symmetry-Bloch's Theorem 175 7.2.1 One Dimension 176 7.2.2 Bloch's Theorem in Three Dimensions 180 7.2.3 Formal Demonstration of Bloch's Theorem 182 7.2.4 Additional Implications of Bloch's Theorem 183 7.2.5 Van Hove Singularities 186 7.2.6 Kronig-Penney Model 189 7.3 Rotational Symmetry-Group Representations 192 7.3.1 Classes and Characters 198 7.3.2 Consequences of point group symmetries for Schroedinger's equation 201 Problems 203 References 206 8 Nearly Free and Tightly Bound Electrons 207 8.1 Introduction 207 8.2 Nearly Free Electrons 208 8.2.1 Degenerate Perturbation Theory 210 8.3 Brillouin Zones 211 8.3.1 Nearly Free Electron Fermi Surfaces 214 8.4 Tightly Bound Electrons 219 8.4.1 Linear Combinations of Atomic Orbitals 219 8.4.2 Wannier Functions 222 8.4.3 Geometric Phases 223 8.4.4 Tight Binding Model 226 Problems 227 References 232 9 Electron-Electron Interactions 233 9.1 Introduction 233 9.2 Hartree and Hartree-Fock Equations 234 9.2.1 Variational Principle 235 9.2.2 Hartree-Fock Equations 235 9.2.3 Numerical Implementation 239 9.2.4 Hartree-Fock Equations for Jellium 242 9.3 Density Functional Theory 244 9.3.1 Thomas-Fermi Theory 247 9.3.2 Stability of Matter 249 9.4 Quantum Monte Carlo 252 9.4.1 Integrals by Monte Carlo 252 9.4.2 Quantum Monte Carlo Methods 253 9.4.3 Physical Results 254 9.5 Kohn-Sham Equations 255 Problems 258 References 262 10 Realistic Calculations in Solids 265 10.1 Introduction 265 10.2 Numerical Methods 266 10.2.1 Pseudopotentials and Orthogonalized Planes Waves (OPW) 266 10.2.2 Linear Combination of Atomic Orbitals (LCAO) 271 10.2.3 Plane Waves 271 10.2.4 Linear Augmented Plane Waves (LAPW) 274 10.3 Definition of Metals, Insulators, and Semiconductors 277 10.4 Brief Survey of the Periodic Table 279 10.4.1 Nearly Free Electron Metals 280 10.4.2 Noble Gases 282 10.4.3 Semiconductors 283 10.4.4 Transition Metals 284 10.4.5 Rare Earths 286 Problems 286 References 291 III MECHANICAL PROPERTIES 293 11 Cohesion of Solids 295 11.1 Introduction 295 11.1.1 Radii of Atoms 297 11.2 Noble Gases 299 11.3 Tonic Crystals 301 11.3.1 EwaldSums 302 11.4 Metals 305 11.4.1 Use of Pseudopotentials 307 11.5 Band Structure Energy 308 11.5.1 Peierls Distortion 309 11.5.2 Structural Phase Transitions 311 11.6 Hydrogen-Bonded Solids 312 11.7 Cohesive Energy from Band Calculations 312 11.8 Classical Potentials 313 Problems 315 References 318 12 Elasticity 321 12.1 Introduction 321 12.2 Nonlinear Elasticity 321 12.2.1 Rubber Elasticity 322 12.2.2 Larger Extensions of Rubber 324 12.3 Linear Elasticity 325 12.3.1 Solids of Cubic Symmetry 326 12.3.2 Isotropic Solids 328 12.4 Other Constitutive Laws 332 12.4.1 Liquid Crystals 332 12.4.2 Granular Materials 335 Problems 336 References 339 13 Phonons 341 13.1 Introduction 341 13.2 Vibrations of a Classical Lattice 342 13.2.1 Classical Vibrations in One Dimension 342 13.2.2 Classical Vibrations in Three Dimensions 346 13.2.3 Normal Modes 347 13.2.4 Lattice with a Basis 348 13.3 Vibrations of a Quantum-Mechanical Lattice 351 13.3.1 Phonon Specific Heat 354 13.3.2 Einstein and Debye Models 358 13.3.3 Thermal Expansion 361 13.4 Inelastic Scattering from Phonons 363 13.4.1 Neutron Scattering 364 13.4.2 Formal Theory of Neutron Scattering 366 13.4.3 Averaging Exponentials 370 13.4.4 Evaluation of Structure Factor 372 13.4.5 Kohn Anomalies 373 13.5 The Moessbauer Effect 374 Problems 376 References 377 14 Dislocations and Cracks 379 14.1 Introduction 379 14.2 Dislocations 381 14.2.1 Experimental Observations of Dislocations 383 14.2.2 Force to Move a Dislocation 386 14.2.3 One-Dimensional Dislocations: Frehkel-Kontorova Model 386 14.3 Two-Dimensional Dislocations and Hexatic Phases 389 14.3.1 Impossibility of Crystalline Order in Two Dimensions 389 14.3.2 Orientational Order 391 14.3.3 Kosterlitz-Thouless-Berezinskii Transition 392 14.4 Cracks 399 14.4.1 Fracture of a Strip 399 14.4.2 Stresses Around an Elliptical Hole 402 14.4.3 Stress Intensity Factor 404 14.4.4 Atomic Aspects of Fracture 405 Problems 406 References 409 15 Fluid Mechanics 413 15.1 Introduction 413 15.2 Newtonian Fluids 413 15.2.1 Euler's Equation 413 15.2.2 Navier-Stokes Equation 415 15.3 Polymeric Solutions 416 15.4 Plasticity 423 15.5 Superfluid 4He 427 15.5.1 Two-Fluid Hydrodynamics 430 15.5.2 Second Sound 431 15.5.3 Direct Observation of Two Fluids 433 15.5.4 Origin of Superfluidity 434 15.5.5 Lagrangian Theory of Wave Function 439 15.5.6 Superfluid 3He 442 Problems 443 References 447 IV ELECTRON TRANSPORT 451 16 Dynamics of Bloch Electrons 453 16.1 Introduction 453 16.1.1 Drude Model 453 16.2 Semiclassical Electron Dynamics 455 16.2.1 Bloch Oscillations 456 16.2.2 k-p Method 457 16.2.3 Effective Mass 459 16.3 Noninteracting Electrons in an Electric Field 459 16.3.1 Zener Tunneling 462 16.4 Semiclassical Equations from Wave Packets 465 16.4.1 Formal Dynamics of Wave Packets 465 16.4.2 Dynamics from Lagrangian 467 16.5 Quantizing Semiclassical Dynamics 470 16.5.1 Wannier-Stark Ladders 472 16.5.2 de Haas-van Alphen Effect 473 16.5.3 Experimental Measurements of Fermi Surfaces 474 Problems 477 References 480 17 Transport Phenomena and Fermi Liquid Theory 4S3 17.1 Introduction 483 17.2 Boltzmann Equation 483 17.2.1 Boltzmann Equation 485 17.2.2 Including Anomalous Velocity 486 17.2.3 Relaxation Time Approximation 487 17.2.4 Relation to Rate of Production of Entropy 489 17.3 Transport Symmetries 490 17.3.1 Onsager Relations 491 17.4 Thermoelectric Phenomena 492 17.4.1 Electrical Current 492 17.4.2 Effective Mass and Holes 494 17.4.3 Mixed Thermal and Electrical Gradients 495 17.4.4 Wiedemann-Franz Law 496 17.4.5 Thermopower-Seebeck Effect 497 17.4.6 Peltier Effect 498 17.4.7 Thomson Effect 498 17.4.8 Hall Effect 500 17.4.9 Magnetoresistance 502 17.4.10 Anomalous Hall Effect 503 17.5 Fermi Liquid Theory 504 17.5.1 Basic Ideas 504 17.5.2 Statistical Mechanics of Quasi-Particles 506 17.5.3 Effective Mass 508 17.5.4 Specific Heat 510 17.5.5 Fermi Liquid Parameters 511 17.5.6 Traveling Waves 512 17.5.7 Comparison with Experiment in 3He 515 Problems 516 References 520 18 Microscopic Theories of Conduction 523 18.1 Introduction 523 18.2 Weak Scattering Theory of Conductivity 523 18.2.1 Genera] Formula for Relaxation Time 523 18.2.2 Matthiessen's Rule 528 18.2.3 Fluctuations 529 18.3 Metal-Insulator Transitions in Disordered Solids 530 18.3.1 Impurities and Disorder 530 18.3.2 Non-Compensated Impurities and the Mott Transition . . 531 18.4 Compensated Impurity Scattering and Green's Functions 534 18.4.1 Tight-Binding Models of Disordered Solids 534 18.4.2 Green's Functions 536 18.4.3 Single Impurity 539 18.4.4 Coherent Potential Approximation 541 18.5 Localization 542 18.5.1 Exact Results in One Dimension 544 18.5.2 Scaling Theory of Localization 547 18.5.3 Comparison with Experiment 551 18.6 Luttinger Liquids 553 18.6.1 Density of States 557 Problems 560 References 564 19 Electronics 567 19.1 Introduction 567 19.2 Metal Interfaces 568 19.2.1 Work Functions 569 19.2.2 Schottky Barrier 570 19.2.3 Contact Potentials 572 19.3 Semiconductors 574 19.3.1 Pure Semiconductors 575 19.3.2 Semiconductor in Equilibrium 578 19.3.3 Intrinsic Semiconductor 580 19.3.4 Extrinsic Semiconductor 581 19.4 Diodes and Transistors 583 19.4.1 Surface States 586 19.4.2 Semiconductor Junctions 587 19.4.3 Boltzmann Equation for Semiconductors 590 19.4.4 Detailed Theory of Rectification 592 19.4.5 Transistor 595 19.5 Inversion Layers 598 19.5.1 Heterostructures 598 f 9,5.2 Quantum Point Contact 600 19.5.3 Quantum Dot 603 Problems 606 References 607 V OPTICAL PROPERTIES 609 20 Phenomenological Theory 611 20.1 Introduction 611 20.2 Maxwell's Equations 613 20.2.1 Traveling Waves 615 20.2.2 Mechanical Oscillators as Dielectric Function 616 20.3 Kramers-Kronig Relations 618 20.3.1 Application to Optical Experiments 620 20.4 The Kubo-Greenwood Formula 623 20.4.1 Bom Approximation 623 20.4.2 Susceptibility 627 20.4.3 Many-Body Green Functions 628 Problems 628 References 631 21 Optical Properties of Semiconductors 633 21.1 Introduction 633 21.2 Cyclotron Resonance 633 21.2.1 Electron Energy Surfaces 636 21.3 Semiconductor Band Gaps 638 21.3.1 Direct Transitions 638 21.3.2 Indirect Transitions 639 21.4 Excitons 641 21.4.1 Mott-Wannier Excitons 641 21.4.2 Frenkel Excitons 644 21.4.3 Electron-Hole Liquid 645 21.5 Optoelectronics 645 21.5.1 SolarCells 645 21.5.2 Lasers 646 Problems 652 References 656 22 Optical Properties of Insulators 659 22.1 Introduction 659 22.2 Polarization 659 22.2.1 Ferroelectrics 659 22.2.2 Berry phase theory of polarization 661 22.2.3 Clausius-Mossotti Relation 661 22.3 Optical Modes in Ionic Crystals 664 22.3.1 Polaritons 666 22.3.2 Polarons 669 22.3.3 Experimental Observations of Polarons 674 22.4 Point Defects and Color Centers 674 22.4.1 Vacancies 675 22.4.2 F Centers 676 22.4.3 Electron Spin Resonance and Electron Nuclear Double Res-onance 677 22.4.4 Other Centers 679 22.4.5 Franck-Condon Effect 679 22.4.6 Urbach Tails 683 Problems 684 References 686 23 Optical Properties of Metals and Inelastic Scattering 689 23.1 Introduction 689 23.1.1 Plasma Frequency 689 23.2 Metals at Low Frequencies 692 23.2.1 Anomalous Skin Effect 694 23.3 Plasmons 695 23.3.1 Experimental Observation of Plasmons 696 23.4 Interband Transitions 698 23.5 Brillouin and Raman Scattering 701 23.5.1 Brillouin Scattering 702 23.5.2 Raman Scattering 703 23.5.3 Inelastic X-Ray Scattering 703 23.6 Photoemission 703 23.6.1 Measurement of Work Functions 703 23.6.2 Angle-Resolved Photoemission 706 23.6.3 Core-Level Photoemission and Charge-Transfer Insulators 710 Problems 716 References 719 VI MAGNETISM 721 24 Classical Theories of Magnetism and Ordering 723 24.1 Introduction 723 24.2 Three Views of Magnetism 723 24.2.1 From Magnetic Moments 723 24.2.2 From Conductivity 724 24.2.3 From a Free Energy 725 24.3 Magnetic Dipole Moments 727 24.3.1 Spontaneous Magnetization of Ferromagnets 730 24.3.2 Ferrimagnets 731 24.3.3 Antiferromagnets 733 24.4 Mean Field Theory and the Ising Model 734 24.4.1 Domains 736 24.4.2 Hysteresis 739 24.5 Other Order-Disorder Transitions 740 24.5.1 Alloy Superlattices 740 24.5.2 Spin Glasses 743 24.6 Critical Phenomena 743 24.6.1 Landau Free Energy 744 24.6.2 Scaling Theory 750 Problems 754 References 757 25 Magnetism of Ions and Electrons 759 25.1 Introduction 759 25.2 Atomic Magnetism 761 25.2.1 Hund's Rules 762 25.2.2 Curie's Law 766 25.3 Magnetism of the Free-El ectron Gas 769 25.3.1 Pauli Paramagnetism 770 25.3.2 Landau Diamagnetism 771 25.3.3 Aharonov-Bohm Effect 774 25.4 Tightly Bound Electrons in Magnetic Fields Ill 25.5 Quantum Hall Effect 780 25.5.1 Integer Quantum Hall Effect 780 25.5.2 Fractional Quantum Hall Effect 785 Problems 791 References 794 26 Quantum Mechanics of Interacting Magnetic Moments 797 26.1 Introduction 797 26.2 Origin of Ferromagnetism 797 26.2.1 Heitler-London Calculation 797 26.2.2 Spin Hamiltonian 802 26.3 Heisenberg Model 802 26.3.1 Indirect Exchange and Superexchange 804 26.3.2 Ground State 805 26.3.3 Spin Waves 805 26.3.4 Spin Waves in Antiferromagnets 808 26.3.5 Comparison with Experiment 811 26.4 Ferromagnetism in Transition Metals 811 26.4.1 Stoner Model 811 26.4.2 Calculations Within Band Theory 813 26.5 Spintronics 815 26.5.1 Giant Magnetoresistance 815 26.5.2 Spin Torque 816 26.6 Kondo Effect 819 26.6.1 Scaling Theory 824 26.7 Hubbard Model 828 26.7.1 Mean-Field Solution 829 Problems 832 References 835 27 Superconductivity 839 27.1 Introduction 839 27.2 Phenomenology of Superconductivity 840 27.2.1 Phenomenological Free Energy 841 27.2.2 Thermodynamics of Superconductors 843 27.2.3 Landau-Ginzburg Free Energy 844 27.2.4 Type I and Type II Superconductors 845 27.2.5 Flux Quantization 850 27.2.6 The Josephson Effect 852 27.2.7 Circuits with Josephson Junction Elements 854 27.2.8 SQUIDS 855 27.2.9 Origin of Josephson's Equations 856 27.3 Microscopic Theory of Superconductivity 858 27.3.1 Electron-Ion Interaction 859 27.3.2 Instability of the Normal State: Cooper Problem 863 27.3.3 Self-Consistent Ground State 865 27.3.4 Thermodynamics of Superconductors 869 27.3.5 Superconductor in External Magnetic Field 873 27.3.6 Derivation of Meissner Effect 876 27.3.7 Comparison with Experiment 879 27.3.8 High-Temperature Superconductors 881 Problems 888 References 890 APPENDICES 895 A Lattice Sums and Fourier Transforms 897 A. l One-Dimensional Sum 897 A. 2 Area Under Peaks 897 A. 3 Three-Dimensional Sum 898 A. 4 Discrete Case 899 A.5 Convolution 900 A. 6 Using the Fast Fourier Transform 900 References 902 B Variational Techniques 903 B. l Functionals and Functional Derivatives 903 B. 2 Time-Independent Schrodinger Equation 904 B. 3 Time-Dependent Schrodinger Equation 905 B. 4 Method of Steepest Descent 906 References 906 C Second Quantization 907 C. l Rules 907 C. 1.1 States 907 C. l.2 Operators 907 C. l.3 Hamiltonians 908 C.2 Derivations 909 C.2.1 Bosons 909 C.2.2 Fermions 910 Index

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