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Preface | |
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Acknowledgments | |
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Crystalline solids | |
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Atomic structure of crystals | |
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Building crystals from atoms | |
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Atoms with no valence electrons | |
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Atoms with s valence electrons | |
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Atoms with s and p valence electrons | |
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Atoms with s and d valence electrons | |
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Atoms with s, d and f valence electrons | |
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Solids with two types of atoms | |
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Hydrogen: a special one-s-valence-electron atom | |
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Solids with many types of atoms | |
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Bonding in solids | |
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Further reading | |
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Problems | |
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The single-particle approximation | |
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The hamiltonian of the solid | |
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The Hartree and Hartree--Fock approximations | |
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The Hartree approximation | |
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Example of a variational calculation | |
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The Hartree--Fock approximation | |
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Hartree--Fock theory of free electrons | |
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The hydrogen molecule | |
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Density Functional Theory | |
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Electrons as quasiparticles | |
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Quasiparticles and collective excitations | |
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Thomas--Fermi screening | |
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The ionic potential | |
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Further reading | |
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Problems | |
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Electrons in crystal potential | |
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Periodicity--Bloch states | |
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k-space--Brillouin zones | |
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Dynamics of crystal electrons | |
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Crystal electrons in an electric field | |
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Crystal symmetries beyond periodicity | |
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Groups and symmetry operators | |
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Symmetries of the band structure | |
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Symmetries of 3D crystals | |
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Special k-points | |
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Further reading | |
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Problems | |
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Band structure of crystals | |
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The tight-binding approximation | |
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Example: 1D linear chain with s or p orbitals | |
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Example: 2D square lattice with s and p orbitals | |
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Generalizations of the TBA | |
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General band-structure methods | |
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Band structure of representative solids | |
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A 2D solid: graphite--a semimetal | |
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3D covalent solids: semiconductors and insulators | |
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3D metallic solids | |
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Further reading | |
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Problems | |
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Applications of band theory | |
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Density of states | |
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Tunneling at metal--semiconductor contact | |
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Optical excitations | |
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Conductivity and dielectric function | |
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Excitons | |
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Energetics and dynamics | |
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The total energy | |
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Forces and dynamics | |
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Further reading | |
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Problems | |
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Lattice vibrations | |
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Phonon modes | |
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The force-constant model | |
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Example: phonons in 2D periodic chain | |
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Phonons in a 3D crystal | |
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Phonons as harmonic oscillators | |
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Application: the specific heat of crystals | |
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The classical picture | |
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The quantum mechanical picture | |
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The Debye model | |
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Thermal expansion coefficient | |
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Application: phonon scattering | |
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Phonon scattering processes | |
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The Debye-Waller factor | |
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The Mossbauer effect | |
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Problems | |
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Magnetic behavior of solids | |
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Magnetic behavior of insulators | |
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Magnetic behavior of metals | |
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Magnetization in Hartree-Fock free-electron gas | |
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Magnetization of band electrons | |
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Heisenberg spin model | |
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Ground state of the Heisenberg ferromagnet | |
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Spin waves in the Heisenberg ferromagnet | |
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Heisenberg antiferromagnetic spin model | |
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Magnetic order in real materials | |
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Crystal electrons in an external magnetic field | |
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de Haas-van Alphen effect | |
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Classical and quantum Hall effects | |
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Further reading | |
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Problems | |
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Superconductivity | |
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Overview of superconducting behavior | |
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Thermodynamics of the superconducting transition | |
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BCS theory of superconductivity | |
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Cooper pairing | |
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BCS ground state | |
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BCS theory at finite temperature | |
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The McMillan formula for T[subscript c] | |
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High-temperature superconductors | |
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Further reading | |
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Problems | |
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Defects, non-crystalline solids and finite structures | |
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Defects I: point defects | |
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Intrinsic point defects | |
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Energetics and electronic levels | |
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Defect-mediated diffusion | |
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Extrinsic point defects | |
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Impurity states in semiconductors | |
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Effect of doping in semiconductors | |
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The p-n junction | |
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Metal-semiconductor junction | |
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Further reading | |
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Problems | |
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Defects II: line defects | |
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Nature of dislocations | |
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Elastic properties and motion of dislocations | |
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Stress and strain fields | |
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Elastic energy | |
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Peierls-Nabarro model | |
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Brittle versus ductile behavior | |
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Stress and strain under external load | |
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Brittle fracture - Griffith criterion | |
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Ductile response - Rice criterion | |
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Dislocation-defect interactions | |
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Further reading | |
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Problems | |
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Defects III: Surfaces and interfaces | |
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Experimental study of surfaces | |
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Surface reconstruction | |
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Dimerization: the Si(001) surface | |
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Relaxation: the GaAs(110) surface | |
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Adatoms and passivation: the Si(111) surface | |
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Growth phenomena | |
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Interfaces | |
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Grain boundaries | |
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Hetero-interfaces | |
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Further reading | |
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Problems | |
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Non-crystalline solids | |
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Quasicrystals | |
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Amorphous solids | |
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Continuous random network | |
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Radial distribution function | |
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Electron localization due to disorder | |
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Polymers | |
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Structure of polymer chains and solids | |
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The glass and rubber states | |
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Further reading | |
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Problems | |
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Finite structures | |
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Clusters | |
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Metallic clusters | |
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Carbon clusters | |
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Carbon nanotubes | |
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Other covalent and mixed clusters | |
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Biological molecules and structures | |
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The structure of DNA and RNA | |
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The structure of proteins | |
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Relationship between DNA, RNA and proteins | |
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Protein structure and function | |
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Further reading | |
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Problems | |
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Appendices | |
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Elements of classical electrodynamics | |
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Electrostatics and magnetostatics | |
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Fields in polarizable matter | |
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Electrodynamics | |
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Electromagnetic radiation | |
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Further reading | |
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Elements of quantum mechanics | |
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The Schrodinger equation | |
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Bras, kets and operators | |
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Solution of the TISE | |
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Free particles | |
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Harmonic oscillator potential | |
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Coulomb potential | |
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Spin angular momentum | |
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Stationary perturbation theory | |
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Non-degenerate perturbation theory | |
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Degenerate perturbation theory | |
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Time-dependent perturbation theory | |
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The electromagnetic field term | |
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Further reading | |
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Problems | |
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Elements of thermodynamics | |
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The laws of thermodynamics | |
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Thermodynamic potentials | |
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Application: phase transitions | |
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Problems | |
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Elements of statistical mechanics | |
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Average occupation numbers | |
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Classical Maxwell-Boltzmann statistics | |
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Quantum Fermi-Dirac statistics | |
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Quantum Bose-Einstein statistics | |
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Ensemble theory | |
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Definition of ensembles | |
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Derivation of thermodynamics | |
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Applications of ensemble theory | |
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Equipartition and the Virial | |
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Ideal gases | |
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Spins in an external magnetic field | |
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Further reading | |
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Problems | |
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Elements of elasticity theory | |
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The strain tensor | |
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The stress tensor | |
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Stress-strain relations | |
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Strain energy density | |
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Applications of elasticity theory | |
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Isotropic elastic solid | |
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Plane strain | |
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Solid with cubic symmetry | |
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Further reading | |
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Problems | |
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The Madelung energy | |
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Potential of a gaussian function | |
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The Ewald method | |
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Problems | |
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Mathematical tools | |
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Differential operators | |
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Power series expansions | |
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Functional derivatives | |
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Fourier and inverse Fourier transforms | |
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The [delta]-function and its Fourier transform | |
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The [delta]-function and the [theta]-function | |
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Fourier transform of the [delta]-function | |
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The [delta]-function sums for crystals | |
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Normalized gaussians | |
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Nobel prize citations | |
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Units and symbols | |
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References | |
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Index | |