Solid State Physics Homework
- Homework #1 (due Monday, Sept. 11), 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. 11 - come prepared with questions and comments. Write a paragraph (in MSWord or LaTex) describing the experiment and the observation.
- Homework #2 (due Monday, Sept. 18), 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.
- Homework #3 (due Monday, Sept. 25), 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. Write a paragraph describing the essential ideas (not formulas!) of liquid crystal elasticity.
- Homework #4 (due Monday, Oct. 2), special problems on elasticity. Read On the Law of Distribution of Energy in the Normal Spectrum by Max Planck. Write a paragraph explaining the crucial contribution this work made to the development of the quantum theory, and its relationship to thermal properties of solids.
- Homework #5 (due Monday, Oct. 16), Ashcroft and Mermin, problems #34.1 (thermodynamics of superconductors) and 34.3 (critical current). Read Tonomura et al., "Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave" (Phys. Rev. Lett. 56, 792 (1986)). Write a paragraph describing the experiment and its results. Discuss whether this experiment verifies the Aharanov-Bohm effect or not. Is the vector potential an observable?
- Homework #6 (due Monday, Oct. 31), 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 Normal modes of aluminum by neutron spectrometry by Brockhouse and Stewart. Write one paragraph explaining how neutron diffraction may be used to measure phonon dispersion relations.
- Homework #7 (due Monday, Nov. 6), Ashcroft and Mermin, problems #22.1(1D chain with long-range interactions), #22.3 (weakly perturbed monatomic lattice). Read Photonic band structure: The face-centered-cubic case by Yablonovitch and Gmitter (see also commentary in Physics Today). Write a paragraph addressing the origin of bands in the photonic case, and comparing and contrasting this result with electronic and phononic band structures.
- Homework #8 (due Monday, Nov. 13),
and 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 11.5 (electronic impurity state). 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 Monday, Nov. 27),
15.1 (nearly free electrons in 1D) and 23.2 (Hubbard antiferromagnetism). Read Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface by Zhang et al. and write a detailed paragraph explaining the physical origin of the topological surface state, and what is meant by "topological". Test your login for WIEN2k (instructions given in class).
- Homework #10 (due Friday, Dec. 1) Carry out a DFT calculation of the band structure of Bi2Se3 in order to demonstrate it is a topological insulator. Follow the instructions at http://euler.phys.cmu.edu/widom/teaching/33-783/w2k.html.
- Homework #11 (due Friday, Dec. 8) Ashcroft and Mermin #12.2 (effective mass) 15.4 (Free electron Fermi sphere for valence 3 FCC), DFT calculations of Fermi surfaces http://euler.phys.cmu.edu/widom/teaching/33-783/fs.html. Choose an original research paper of interest to you. Write a full page summary and critique of the paper, including the theoretical basis and any experimental methods and results. Organize your summary into multiple independent coherent paragraphs. Be sure to include citations to the paper, as well as any supporting material that you use. Figures are optional and if included must be on pages following the summary.
- Midterm #1 Wednesday, October 4, in class
- Midterm #2 Wednesday, Nov. 15, in class
- Final exam Tuesday, December 12, 1-4pm, 5312 Wean Hall
- Sample exams:
33-448 Midterm 1,
33-448 Midterm 2,
33-448 Midterm 3,
33-783 Take Home Midterm,