Solid State Physics Homework
- Homework #1 (due Friday, Sept. 7), Simon problem 3.1a-d (Hall effect), 4.2 (free electron velocity) and 4.7 (free electron energy, pressure and bulk modulus). Read Quantized conductance of point contacts in a two-dimensional electron gas by van Wees, et al. A nice commentary on this work is in Physics Today. We will discuss this paper in the second class hour on Sept. 10 - come prepared with questions and comments.
- Homework #2 (due Friday, Sept. 14), Ashcroft and Mermin problem 1.2 (Joule heating), Simon problem 19.6a (Curie-Langevin paramagnetism, note "monatomic" should be "monovalent"), and a special problem on Landau levels. Read New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance by Klitzing, Dorda and Pepper, and prepare questions about the paper.
- Optional but recommended: Install and run kwant. Play with parameters and novel ideas.
- Homework #3 (due Friday, Sept. 21), Aschroft and Mermin problem 1.3 (Thomson effect) and 1.4 (Helicon waves). Read Liquid crystals. On the theory of liquid crystals by F.C. Frank. Focus on the essential ideas (not formulas!) of liquid crystal elasticity.
- Homework #4 (due Friday, Sept. 28), special problems on elasticity. Read On the Law of Distribution of Energy in the Normal Spectrum by Max Planck. Think about the crucial contribution this work made to the development of the quantum theory, and its relationship to thermal properties of solids.
- Homework #5 (due Friday, Oct. 12), Special problem on quantized thermal conductance. Ashcroft and Mermin, problems #34.1 (thermodynamics of superconductors) and 34.3 (critical current).
Read Composite-fermion approach for the fractional quantum Hall effect by Jain. See also figure 1 in Introduction to the fractional quantum Hall effect by Girvin.
- Homework #6 (due Wednesday, Oct. 24), Simon, problems 12.3 (zincblende structure), 13.3 (directions and spacings of crystal planes), 14.7 (lattice and basis), and 14.9 (form factor).
Read Indexing problems in quasicrystal diffraction by Elser. Prepare questions to discuss in class.
- Homework #7 (due Friday, Nov. 2), Ashcroft and Mermin, problems #22.1(1D chain with long-range interactions), #22.3 (weakly perturbed monatomic lattice). Kittel, problem #4.4 (Kohn anomaly). Read Photonic band structure: The face-centered-cubic case by Yablonovitch and Gmitter (see also commentary in Physics Today), and prepare questions for discussion in class.
- Optional but recommended: Revisit kwant to solve tight-binding models for graphene and for the spin Hall effect.
- Homework #8 (due Friday, Nov. 16),
Simon problems 9.4 (decaying wave) and 9.6 (impurity mode, note q is NOT real, discuss also the case of M>m and sketch the mode in each case). Simon 11.4 (multiorbital atom) and Simon 11.5 (electronic impurity state, note relation to 9.6). Read Energy levels and wavefunctions of Bloch electrons in rational and irrational magnetic fields By Hofstadter and write a paragraph summarizing the models considered and the physical origin of the intricate band structure observed. You might also be interested in this article in Physics Today. Make a list of questions you would like to ask during class discussion.
- Homework #9 (due Wednesday, Nov. 28),
Simon problems 15.1 (nearly free electrons in 1D), 23.2 (Hubbard antiferromagnetism), and Ashcroft and Mermin #12.2 (effective mass) 15.4 (Free electron Fermi sphere for valence 3 FCC).
- Homework #10 (due Wednesday, Dec. 5) Carry out a DFT calculation of the electronic structure and Fermi surfaces of elemental Cu and Al. Follow the instructions at http://euler.phys.cmu.edu/widom/teaching/33-783/fs.html.
- Optional: Read a paper and carry out a calculation on the topological insulator Bi2Se3.
Exams
- Midterm #1, Friday, October 5, in class
- Midterm #2, Wednesday, Nov. 7, in class
- Final exam, Tuesday, Dec. 11, 1-4:00pm, room Wean Hall 4709
- Sample exams:
Midterm 1,
Midterm 2,
Final