Course Outline: Download here.
Class Timings and Venue: 09:30 a.m. to 10:45 a.m., Tuesday and Thursday
Office Hours: 03:00 p.m. to 04:00 p.m., Tuesday and Thursday
Class TA: Muzamil Shah and Touqeer Zahid
Describing the crystalline state (5 lectures)
- Lecture 1:
Symmetry elements and symmetry operations by Sabieh Anwar | Video - Lecture 2: Development of point groups | Video
- Lecture 3: How point groups lead to crystal systems and Bravais Lattice | Video
- Lecture 4: The concept of space groups | Video
- Lecture 5: Important crystal structures | Video
- Homework 1 | Solution.
- Homework 2 | Solution
- EPFL Switzerland had an online interactive Crystallography course. This is a wonderful resource for delving deeper into crystallography and will also motivate ideas for projects in computational physics.
- Nice tutorial on understanding the nomenclature of space groups and International Tables How to read (and understand) Volume 1 of International Tables of Crystallography, J. Appl. Cryst. 43 1150-1171 (2010), by Z. Dauter and M. Jaskolski.
- Nature Milestones on Crystallography
- Handout on point groups taken from “Solid State Physics” by Gerald Burns.
- Handout on space groups taken from the International Tables for Crystallography.
- Handout on space groups for the most important cubic structures and the wurtzite structure also taken from the International Tables for Crystallography.
- Learning about point groups: check this wonderful resource at Otterbein University. We also use this in class to understand the symmetry operations associated with the various point groups.
- Download and test the self-explanatory software Crystalline Solids for visualization the seven crystal classes as well as close packing of atoms.
Diffraction and the reciprocal lattice (5 lectures)
- Lecture 6: Planes and directions inside a crystal | Video
- Lecture 7: The reciprocal lattice | Video
- Lecture 8: Diffraction and the usefulness of the reciprocal lattice | Video
- Lecture 9: The reciprocal lattice as a Fourier transform of the direct lattice | Video
- Lecture 10: Fourier transform of the basis and systematic absences | Video
- Homework 3 | Solution
- Homework 4 | Solution
- Homework 5 | Solution
- I have shared the book The Structure of Crystals by A.M. Glaser. This is a concise summary of the concepts we’ve covered, particularly relevant to viewing diffraction as a phenomenon in the reciprocal space.
Independent free electrons (3 lectures)
- Lecture 11: Quantized free electrons in metals | Video
- Lecture 12: Thermal properties of quantized energy electrons | Video
- Lecture 13: Landau quantization | Video
Non-free but still independent electrons in a periodic potential (5 lectures)
- Lecture 14: Weak perturbation: introducing band gaps | Video
- Lecture 15: Effective mass of electrons inside a periodic potential | Video
- Lecture 16: The Bloch theorem | Video
- Lecture 17: Brillouin Zones | Video
- Lecture 18: Fermi surfaces | Video
- Also see my lecture 23 (further down in the list!)
- Homework 6 | Solution
- Homework 7 | Solution
- An excellent compilation of three-dimensional Fermi surfaces can be seen here: The Fermi Surface Database at the University of Florida’s Physics Department’s website.
- Students need to be aware of the time-independent perturbation theory, both nondegenerate and degenerate. My personal favorite is Chapter 14 of Mark Beck’s book: Quantum Mechanics: Theory and Experiment. Alternatively, you can see my lectures on non-degenerate perturbation theory.
- The visualization of higher order Brillouin Zones is quite an interesting pastime or full-time hobby. Higher Brillouin Zones by Andrew, Salagaram and Chetty published in the European Journal of Physics.
Tight-binding model and phonons (4 lectures)
- Lecture 19: Tight binding model: H2+ molecule and monoatomic chain | Video
- Lecture 20: Diatomic chain and two bands example | Video
- Lecture 21: Elastic waves: monatomic and diatomic chain | Video
- Lecture 22: Concept of the phonon | Video
- Lecture 23: Electronic structure of graphene | Video
- Homework 8 (ungraded)
- The web is replete with discussions on the electronic properties of graphene such as: Tight binding model for graphene by Franz Utermohlen and Introduction to the physical properties of graphene by J. Fuchs and M.O. Goerbig
- Here is my Mathematica notebook (pdf version) that calculates the band structure of graphene.
Seminconductors (3 lectures)
- Lecture 24: Introduction to semiconductors | Video
- Lecture 25: Electrical conductivity in semiconductors | Video
Text books:
- The Oxford Solid State Basics by Steven H. Simon
- Selected topics from: Band Theory and Electronic Properties of Solids by J. Singleton (Oxford University Press) 2006.