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0 (hodnocen0 x )

BK

First published

Cambridge : Cambridge University Press, 2019

xxiii, 653 stran : ilustrace (některé barevné) ; 26 cm

ISBN 978-0-521-11711-1 (vázáno)

Obsahuje bibliografie a rejstřík

001635970

Contents // List of Figures page x // List of Tables xviii // Preface xxi // Acknowledgments xxin // 1 From Atoms to Solids 1 // 1.1 Electronic Structure of Atoms 2 // 1.2 Forming Bonds Between Atoms 5 // 1.2.1 The Essence of Metallic Bonding: The Frcc-Electron Model 6 // 1.2.2 The Essence of Covalent Bonding 10 // 1.2.3 Other Types of Bonding in Solids 14 // 1.3 The Architecture of Crystals 15 // 1.3.1 Atoms with No Valence Electrons 16 // 1.3.2 Atoms with s Valence Electrons 21 // 1.3.3 Atoms with s and p Valence Electrons 23 // 1.3.4 Atoms with s and d Valence Electrons 32 // 1.3.5 Atoms with s4 d, and/ Valence Electrons 33 // 1.3.6 Solids with Two Types of Atoms 33 // 1.3.7 Hydrogen: A Special One-s1-Valence-Electron Atom 37 // 1.3.8 Solids with More Than Two Types of Atoms 39 // 1.4 Bonding in Solids 41 // Further Reading 45 // Problems 46 // 2 Electrons in Crystals: Translational Periodicity 52 // 2.1 Translational Periodicity: Bloch States 52 // 2.2 Reciprocal Space: Brillouin Zones 59 // 2.2.1 Nature of Wave-Vector ? 59 // 2.2.2 Brillouin Zones and Bragg Planes 60 // 2.2.3 Periodicity in Reciprocal Space 65 // 2.2.4 Symmetries Beyond Translational Periodicity 66 // 2.3 The Free-Electron and Nearly Free-Electron Models 69 // 2.4 Effective Mass, “k • p” Perturbation Theory 75 // 2.5 The Tight-Binding Approximation 76 // 2.5.1 Generalizations of the TBA 96 // 2.6 General Band-Structure Methods 99 // v // Contents // 2.6.1 Crystal Pseudopotentials 103 // 2.7 Localized

Wannier Functions 105 // 2.8 Density of States 107 // 2.8.1 Free-Electron Density of States 110 // 2.8.2 Local Density of States 111 // 2.8.3 Crystal DOS: Van Hove Singularities 112 // Further Reading 115 // Problems 116 // 3 Symmetries Beyond Translational Periodicity 119 // 3.1 Time-Reversal Symmetry for Spinless Fermions 119 // 3.2 Crystal Groups: Definitions 121 // 3.3 Symmetries of 3D Crystals 124 // 3.4 Symmetries of the Band Structure 129 // 3.5 Application: Special k-Points 135 // 3.6 Group Representations 137 // 3.7 Application: The N-F-Center in Diamond 155 // Further Reading 159 // Problems 159 // 4 From Many Particles to the Single-Partide Picture 161 // 4.1 The Hamiltonian of the Solid 162 // 4.1.1 Bom-Oppenheimer Approximation 163 // 4.2 The Hydrogen Molecule 166 // 4.3 The Hartree and Hartree-Fock Approximations 173 // 4.3.1 The Hartree Approximation 173 // 4.3.2 The Hartree-Fock Approximation 176 // 4.4 Hartree-Fock Theory of Free Electrons 178 // 4.5 Density Functional Theory 182 // 4.5.1 Thomas-Fermi-Dirac Theory’ 182 // 4.5.2 General Formulation of DFT 183 // 4.5.3 Single-Particle Equations in DFT 186 // 4.5.4 The Exchange-Correlation Term in DFT 189 // 4.5.5 Time-Dependent DFT 193 // 4.6 Quasiparticles and Collective Excitations 195 // 4.7 Screening: The Thomas-Fermi Model 197 // 4.8 Quasiparticle Energies: GW Approximation 199 // 4.9 The Pseudopotential 202 // 4.10 Energetics and Ion Dynamics 208 // 4.10.1 The Total Energy 208 // 4.10.2 Forces and Ion Dynamics

218 // Further Reading 221 // Problems 222 // VII // Contents // 5 Electronic Properties of Crystals 227 // 5.1 Band Structure of Idealized 1D Solids 227 // 5.1.1 A Finite “ID Solid”: Benzene 227 // 5.1.2 An infinite “ID Solid”: Polyacetylcne 231 // 5.2 2D Solids: Graphene and Beyond 235 // 5.2.1 Carbon Nanotubes 239 // 5.3 3D Metallic Solids 244 // 5.4 3D Ionic and Covalent Solids 248 // 5.5 Dopingofldeal Crystals 256 // 5.5.1 Envelope Function Approximation 256 // 5.5.2 Effect of Doping in Semiconductors 261 // 5.5.3 The p-n Junction 265 // 5.5.4 Metal-Scmiconductor Junction 273 // Further Reading 276 // Problems 276 // 6 Electronic Excitations 280 // 6.1 Optical Excitations 280 // 6.2 Conductivity and Dielectric Function 284 // 6.2.1 General Formulation 285 // 6.2.2 Drude and Lorentz Models 286 // 6.2.3 Connection to Microscopic Features 291 // 6.2.4 Implications for Crystals 293 // 6.2.5 Application: Optical Properties of Metals and Semiconductors 299 // 6.3 Excitons 302 // 6.3.1 General Considerations 303 // 6.3.2 Strongly Bound (Frenkel) Excitons 308 // 6.3.3 Weakly Bound (Wannier) Excitons 311 // Further Reading 316 // Problems 317 // 7 Lattice Vibrations and Deformations 319 // 7.1 Lattice Vibrations: Phonon Modes 319 // 7.2 The Bom Force-Constant Model 324 // 7.3 Applications of the Force-Constant Model 328 // 7.4 Phonons as Harmonic Oscillators 340 // 7.5 Application: Specific Heat of Crystals 343 // 7.5.1 The Classical Picture 343 // 7.5.2 The Quantum-Mechanical

Picture 344 // 7.5.3 The Debye Model 346 // 7.5.4 Thermal Expansion Coefficient 349 // 7.6 Application: Mössbauer Effect 350 // 7.7 Elastic Deformations of Solids 353 // Contents // 7.7.1 Phenomenological Models of Solid Deformation 354 // 7.7.2 Elasticity Theory: The Strain and Stress Tensors 356 // 7.7.3 Strain Energy Density 361 // 7.7.4 Isotropic Solid 363 // 7.7.5 Solid with Cubic Symmetry 368 // 7.7.6 Thin Plate Equilibrium 369 // 7.8 Application: Phonons of Graphene 371 // Further Reading 375 // Problems 375 // 8 Phonon Interactions 379 // 8.1 Phonon Scattering Processes 379 // 8.1.1 Scattering Formalism 381 // 8.2 Application: The Debye-Waller Factor 385 // 8.3 Phonon Photon Interactions 387 // 8.3.1 Infrared Absorption 389 // 8.3.2 Raman Scattering 390 // 8.4 Phonon-Electron Interactions: Superconductivity 392 // 8.4.1 BCS Theory of Superconductivity 394 // 8.4.2 The McMillan Formula for Tf 411 // 8.4.3 High-Temperature Superconductors 412 // Further Reading 415 // Problems 415 // 9 Dynamics and Topological Constraints 417 // 9.1 Electrons in External Electromagnetic Fields 417 // 9.1.1 Classical Hall Effect 419 // 9.1.2 Landau Levels 421 // 9.1.3 Quantum Hall Effect 424 // 9.1.4 de Haas-van Alphen Effect 431 // 9.2 Dynamics of Crystal Electrons: Single-Band Picture 434 // 9.3 Time-Reversal Invariance 438 // 9.3.1 Kramers Degeneracy 440 // 9.4 Berry’s Phase 440 // 9.4.1 General Formulation 441 // 9.4.2 Berry’s Phase for Electrons in Crystals 446 // 9.5 Applications

of Berry’s Phase 454 // 9.5.1 Aliaronov-Bohrn Effect 454 // 9.5.2 Polarization of Crystals 456 // 9.5.3 Crystal Electrons in Uniform Electric Field 458 // 9.6 Chem Numbers 459 // 9.7 Broken Symmetry and Edge States 463 // 9.7.1 Broken Symmetry in Honeycomb Lattice 463 // 9.7.2 Edge States of Honeycomb Lattice 465 // 9.8 Topological Constraints 469 // Contents // Further Reading 476 // Problems 476 // 10 Magnetic Behavior of Solids 480 // 10.1 Overview of Magnetic Behavior of Insulators 481 // 10.2 Overview of Magnetic Behavior of Metals 486 // 10.2.1 Free Fermions in Magnetic Field: Pauli Paramagnetism 487 // 10.2.2 Magnetization in Hartree-Fock Free-Electron Model 490 // 10.2.3 Magnetization of Band Electrons 493 // 10.3 Classical Spins: Simple Models on a Lattice 497 // 10.3.1 Non-interacting Spins on a Lattice: Negative Temperature 497 // 10.3.2 Interacting Spins on a Lattice: Ising Model 502 // 10.4 Quantum Spins: Heisenberg Model 509 // 10.4.1 Motivation of the Heisenberg Model 510 // 10.4.2 Ground State of Heisenberg Ferromagnet 514 // 10.4.3 Spin Waves in Heisenberg Ferromagnet 516 // 10.4.4 Heisenberg Anti ferromagnetic Spin Model 520 // 10.5 Magnetic Domains 522 // Further Reading 525 // Problems 525 // Appendices 529 // Appendix A Mathematical Tools 531 // Appendix ? Classical Electrodynamics 549 // Appendix C Quantum Mechanics 565 // Appendix D Thermodynamics and Statistical Mechanics 610 // Index // 646