Solid State Physics

1. Electrons in one-dimensional periodic potentials

• 1.1. The Bloch theorem for one-dimensional periodicity
• 1.2. Energy levels of a single quantum well and of a periodic array of quantum wells
• 1.3. Transfer matrix, resonant tunneling and energy bands
• 1.4. The tight-binding model
• 1.5. Plane waves and nearly free-electron model
• 1.6. Some dynamical aspects of electrons in band theory
• Appendix A Solved problems and complements
• Further reading

2. Geometrical description of crystals: direct and reciprocal lattices

• 2.1. Simple lattices and composite lattices
• 2.2. Geometrical description of some crystal structures
• 2.3. Wigner–Seitz primitive cells
• 2.4. Reciprocal lattices
• 2.5. Brillouin zones
• 2.6. Translational symmetry and quantum mechanical aspects
• 2.7. Density-of-states and critical points
• Appendix A Solved problems and complements
• Further reading

3. The Sommerfeld free-electron theory of metals

• 3.1. Quantum theory of the free-electron gas
• 3.2. Fermi–Dirac distribution function and chemical potential
• 3.3. Electronic specific heat in metals and thermodynamic functions
• 3.4. Thermionic emission from metals
• Appendix A Outline of statistical physics and thermodynamic relations
• Appendix B Fermi–Dirac and Bose–Einstein statistics for independent particles
• Appendix C Modified Fermi–Dirac statistics in a model of correlation effects
• Further reading

4. The one-electron approximation and beyond

• 4.1. Introductory remarks on the many-electron problem
• 4.2. The Hartree equations
• 4.3. Identical particles and determinantal wavefunctions
• 4.4. Matrix elements between determinantal states
• 4.5. The Hartree–Fock equations
• 4.6. Overview of approaches beyond the one-electron approximation
• 4.7. Electronic properties and phase diagram of the homogeneous electron gas
• 4.8. The density functional theory and the Kohn–Sham equations
• Appendix A Bielectronic integrals among spin orbitals
• Appendix B Outline of second quantization formalism for identical fermions
• Appendix C An integral on the Fermi sphere
• Appendix D Solved problems and complements
• Further reading

5. Band theory of crystals

• 5.1. Basic assumptions of the band theory
• 5.2. The tight-binding method (LCAO method)
• 5.3. The orthogonalized plane wave (OPW) method
• 5.4. The pseudopotential method
• 5.5. The cellular method
• 5.6. The augmented plane wave (APW) method
• 5.7. The Green’s function method (KKR method)
• 5.8. Iterative methods in electronic structure calculations
• Appendix A Matrix elements of the augmented plane wave method
• Appendix B Solved problems and complements
• Appendix C Evaluation of the structure coefficients of the KKR method with the Ewald procedure
• Further reading

6. Electronic properties of selected crystals

• 6.1. Band structure and cohesive energy of rare-gas solids
• 6.2. Electronic properties of ionic crystals
• 6.3. Covalent crystals with diamond structure
• 6.4. Band structures and Fermi surfaces of some metals
• 6.5. Carbon-based materials and electronic structure of graphene
• Appendix A Solved problems and complements
• Further reading

7. Excitons, plasmons, and dielectric screening in crystals

• 7.1. Exciton states in crystals
• 7.2. Plasmon excitations in crystals
• 7.3. Static dielectric screening in metals within the Thomas–Fermi model
• 7.4. The longitudinal dielectric function within the linear response theory
• 7.5. Dielectric screening within the Lindhard model
• 7.6. Quantum expression of the longitudinal dielectric function in crystals
• 7.7. Surface plasmons and surface polaritons
• Appendix A Friedel sum rule and Fumi theorem
• Appendix B Quantum expression of the longitudinal dielectric function in materials in the linear response theory
• Appendix C Lindhard dielectric function for the free-electron gas
• Appendix D Quantum expression of the transverse dielectric function in materials in the linear response theory
• Further reading

8. Interacting electronic-nuclear systems and the adiabatic principle

• 8.1. Interacting electronic-nuclear systems and adiabatic potential energy surfaces
• 8.2. Non-degenerate adiabatic surface and nuclear dynamics
• 8.3. Degenerate adiabatic surfaces and Jahn–Teller systems
• 8.4. The Hellmann–Feynman theorem and electronic-nuclear systems
• 8.5. Parametric Hamiltonians and Berry phase
• 8.6. The Berry phase theory of the macroscopic electric polarization in crystals
• Appendix A Simplified evaluation of typical Jahn–Teller and Renner–Teller matrices
• Appendix B Solved problems and complements
• Further reading

9. Lattice dynamics of crystals

• 9.1. Dynamics of monatomic one-dimensional lattices
• 9.2. Dynamics of diatomic one-dimensional lattices
• 9.3. Dynamics of general three-dimensional crystals
• 9.4. Quantum theory of the harmonic crystal
• 9.5. Lattice heat capacity. Einstein and Debye models
• 9.6. Considerations on anharmonic effects and melting of solids
• 9.7. Optical phonons and polaritons in polar crystals
• Appendix A Quantum theory of the linear harmonic oscillator
• Further reading

10. Scattering of particles by crystals

• 10.1. General considerations
• 10.2. Elastic scattering of X-rays from crystals and the Thomson approximation
• 10.3. Compton scattering and electron momentum density
• 10.4. Inelastic scattering of particles and phonons spectra of crystals
• 10.5. Quantum theory of elastic and inelastic scattering of neutrons
• 10.6. Dynamical structure factor for harmonic displacements and Debye–Waller factor
• 10.7. Mössbauer effect
• Appendix A Solved problems and complements
• Further reading

11. Optical and transport properties of metals

• 11.1. Macroscopic theory of optical constants in homogeneous materials
• 11.2. The Drude theory of the optical properties of free carriers
• 11.3. Transport properties and Boltzmann equation
• 11.4. Static and dynamic conductivity in metals
• 11.5. Boltzmann treatment and quantum treatment of intraband transitions
• 11.6. The Boltzmann equation in electric fields and temperature gradients
• Appendix A Solved problems and complements
• Further reading

12. Optical properties of semiconductors and insulators

• 12.1. Transverse dielectric function and optical constants in homogeneous media
• 12.2. Quantum theory of band-to-band optical transitions and critical points
• 12.3. Indirect phonon-assisted transitions
• 12.4. Two-photon absorption
• 12.5. Exciton effects on the optical properties
• 12.6. Fano resonances and absorption line shapes
• 12.7. Optical properties of vibronic systems
• Appendix A Transitions rates at first and higher orders of perturbation theory
• Appendix B Optical constants, Green’s function, and Kubo–Greenwood relation
• Further reading

13. Transport in intrinsic and homogeneously doped semiconductors

• 13.1. Fermi level and carrier density in intrinsic semiconductors
• 13.2. Impurity levels in semiconductors
• 13.3. Fermi level and carrier density in doped semiconductors
• 13.4. Non-equilibrium carrier distributions
• 13.5. Generation and recombination of electron-hole pairs in doped semiconductors
• Appendix A Solutions of typical transport equations in uniformly doped semiconductors
• Further reading

14. Transport in inhomogeneous semiconductors

• 14.1. Properties of the p-n junction at equilibrium
• 14.2. Current-voltage characteristics of the p-n junction
• 14.3. The bipolar junction transistor
• 14.4. Semiconductor heterojunctions
• 14.5. Metal-semiconductor contacts
• 14.6. Metal-oxide-semiconductor structure
• 14.7. Metal-oxide-semiconductor field-effect transistor (MOSFET)
• Further reading

15. Electron gas in magnetic fields

• 15.1. Magnetization and magnetic susceptibility
• 15.2. Energy levels and density-of-states of a free electron gas in magnetic fields
• 15.3. Landau diamagnetism and de Haas–van Alphen effect
• 15.4. Spin paramagnetism of a free-electron gas
• 15.5. Magnetoresistivity and classical Hall effect
• 15.6. Quantum Hall effects
• Appendix A Landau diamagnetism
• Appendix B The origin of the Peierls phase
• Appendix C Solved problems and complements
• Further reading

16. Magnetic properties of localized systems and Kondo impurities

• 16.1. Quantum mechanical treatment of magnetic susceptibility
• 16.2. Permanent magnetic dipoles in atoms or ions with partially filled shells
• 16.3. Paramagnetism of localized magnetic moments
• 16.4. Localized magnetic states in normal metals
• 16.5. Dilute magnetic alloys and the resistance minimum phenomenon
• 16.6. Magnetic impurity in normal metals at very low temperatures
• Further reading

17. Magnetic ordering in crystals

• 17.1. Ferromagnetism and the Weiss molecular field
• 17.2. Microscopic origin of the coupling between localized magnetic moments
• 17.3. Antiferromagnetism in the mean field approximation
• 17.4. Spin waves and magnons in ferromagnetic crystals
• 17.5. The Ising model with the transfer matrix method
• 17.6. The Ising model with the renormalization group theory
• 17.7. Itinerant magnetism
• Appendix A Solved problems and complements
• Further reading

18. Superconductivity

• 18.1. Some phenomenological aspects of superconductors
• 18.2. The Cooper pair idea
• 18.3. Ground state for a superconductor in the BCS theory at zero temperature
• 18.4. Excited states of superconductors at zero temperature
• 18.5. Treatment of superconductors at finite temperature and heat capacity
• 18.6. The phenomenological London model for superconductors
• 18.7. Macroscopic quantum phenomena
• 18.8. Tunneling effects
• Appendix A The phonon-induced electron-electron interaction
• Further reading

19. Non-equilibrium Green’s functions for quantum transport

• 19.1. System Hamiltonians, time evolution pictures and current operators
• 19.2. Definition of the Green’s functions
• 19.3. Evaluating the retarded and advanced Green’s functions
• 19.4. The foundations of the Keldysh formalism
• 19.5. Operational expressions for quantum electron transport
• Appendix A Solved problems and complements