Lecture Notes Chapter 0 -- Front Matter (Assessments & TAs) Course outline and book list (including e-books) Important Dates and Guidelines for Self-Study and Presentation part of assessment Chapter 1 -- Overview Chapter II - Part 1 - Crystal Structure I [Lattices, Bravis lattcies, description, primitive vectors, primitive unit cells, Wigner-Seitz cells, conventional unit cells, lattice vectors, simple lattices in 2D and 3D] Chapter II - Part 2 - Crystal Structure I [Cubic lattices, Directions in crystals, Lattice planes, Miler indices, direction normal to a set of planes, distance between adjacent planes] Chapter II (Appendix A) -- Illustrating why 5-fold symmetry is missing in Bravais lattices Chapter II (Appendix B) -- A remark on quasicrystals Chapter III -- Crystal Structures II (decorating lattice points by atoms) Chapter IV -- The Reciprocal Lattice and Brillouin Zone Chapter IV (Appendix A) -- Brillouin Zones Chapter IV (Appendix B) -- Expanding a periodic function using plane waves as an application of reciprocal lattice Chapter V (Part 1) -- Elastic Scattering of Waves in Solids (Basic idea of scattering theory, X-ray diffraction, Laue Condition and Bragg condition) Chapter V (Part 2) -- Examples (SC, FCC, BCC), Ewald construction and ideas on meeting the Laue condition (thus X-ray diffraction methods) Extension I -- Developments to watch in determining crystal structures Chapter VI (Part 1) -- Lattice Vibrations (Phonons) [What is the problem? Born-Oppenheimer/Adiabatic approximation, Review on normal modes] Chapter VI (Part 2) -- Lattice Vibrations (Phonons) [1D monatomic infinite chain (dispersion relation) and what does periodicity do? Finite chain plus periodic boundary conditions (mimic an infinite chain), counting the number of modes] Chapter VI (Part 3) -- Lattice Vibrations [Linear diatomic chain, acoustic branch and optical branch, transverse and longitudinal motions] Chapter VI (Part 4) -- Lattice Vibrations [higher dimenions, counting of branches and modes, ideas on phonons, get ready for counting the density of modes] Chapter VI (Appendix A) -- Quantum Mechanics of a Harmonic Oscillator (short review) Chapter VI (Appendix B) -- Statistical Physics of a collection of independent harmonic oscillators (see PHYS4260) Chapter VI (Appendix C) -- Physical Picture of collective excitations (ground state as vacuum, excited states as a few excitations) Chapter VI (Appendix D) -- Physical Momentum of lattice vibrations Chapter VI (Appendix E) -- General Formalism via the Dynamical Matrix Chapter VI (Appendix F) -- Goldstone mode and Universal behavior Optional Appendix A - A 4-page summary from how to treat discrete chain and a continuous chain quantum mechanically Optional Appendix B -- A 27-page drivations on quantizing a discrete chain and a continuous chain Chapter VII (Part 1) - Thermal Properties of Solids (mostly due to phonons) [Heat capacity of solids, Statistical Physics of phonons (harmonic oscillators), Einstein model] Chapter VII (Part 2) -- The density of states or density of normal modes Chapter VII (Part 3) -- The Debye model (statistical mechanics calculations, the physical picture, a hand-waving argument) Chapter VII (Supplementary) -- A clearer table on data of molar heat capacity of elements at room temperature Chapter VII (Appendices) -- Anharmonic Effects (Thermal expansion and Thermal Conduction in insulators) Chapter VII (Supplementary) - Tables of Data (expansion coefficient, sound speed, thermal conductivity) Extension II -- Phonons (Developments to watch) Chapter XIII (Part 1) -- Free electron model of metals (Periodic BC, density of states, 3D case - Fermi energy, Fermi wavevector, Fermi surface, Fermi-Dirac distribution] Chapter XIII (Part 2) -- Free electron model of metals [Electronic heat capacity, Basic transport quantities, Drude model of conductivity (and optical properties)] Chapter XIII (Appendix) -- Free electron model of metals [Stat Mech calculation of low-temperature heat capacity of an ideal Fermi gas] Chapter IX -- General Discussions on Electronic States in Solids Chapter X (Part 1) -- Energy Band Theory [General Formalism - Plane wave expansion or turning the energy band problem into a huge matrix problem, the nearly free electron model] Chapter X (Part 1) -- Energy Band Theory [Tight Binding Model - Extension the LCAO formalism in molecular physics to solids] Chapter X (Supplement 1) -- Turning a Schrodinger Equation problem into a matrix problem Chapter X (Supplement 2) -- An alternative derivation of the Central Equation in band structure problem using plane waves as the basis set Chapter X (Supplement 3) -- 2x2 matrices cover much physics Chapter X (Supplementary Pages) -- Band Theory and Nearly free energy model (19 March 2013) Chapter X (Extension) -- Graphene Band Structure and Massless Ferimon Chapter X (Extension) -- ABC of Relativistic QM Chapter X (Extension) -- Photonic Band Gap Materials Electronic Bands -- Extension Chapter XI -- After getting the energy bands Chapter XII -- Electron Dynamics [Velocity of an electron in a Bloch state, Full bands do not conduct, Semi-classical equation of motion, Dynamical effective mass]
