Project Topics
Here is a list of possible topics for the final project. More challenging topics are marked with a *, not to scare you off but to indicate that I will be more inclined to discuss them with you in depth than is the norm (I'm happy to discuss any project, but some might need extra guidance to ensure a level playing field.) Email me to claim a topic and it will be noted here - topics that have been struck through have been claimed.
Band theory: Wannier functions and their uses Trenton Salk"Floquet theory": Bloch's theorem for time-periodic systems Adam HanninenChern insulators and the quantum anomalous Hall effect (theory + recent experiments) Jen-Ru ChenKane-Mele model (without Rashba spin-orbit) Alex SternLandau levels in graphene Mason EastmanAngle-resolved photoemission spectroscopy (ARPES) and spin-charge separation in 1D Andrew Yang- "Fourier-space crystallography" and level degeneracies in crystals and quasicrystals
- Polarons (quantitatively in d=1 only)
Resonant Inelastic X-Ray scattering (RIXS): what is it and what does it get us? Chengcen ShaLandauer formalism for ballistic conduction (see Datta's book) Claire GilpinNMR relaxation and Knight shift measurements in solids Kate RodriguezQuasicrystals, theory and experiment David Mallin- *"Heavy fermion" materials
Phonons in nanocrystals Sam KeeneBasic Kondo physics Anerudh Kannan- *
Landau's Fermi liquid theory Aaron Friedman Basics of magnetism: ferromagnets/antiferromagnets. Alan Tam*Majorana bound states in 1D superconductors (note: here you may need to learn a bit about superconductivity, but the heart of the problem is still a tight-binding chain) Peter Wagner- *Laughlin's wavefunction for the fractional quantum Hall effect
- *Soliton excitations in polyacetylene (connected to the Peierls' transition discussed in class)
*Spin-orbit coupled semiconductor thin films: Rashba dispersion and persistent spin helix Calvin Lau- *
Hopping conduction in disordered systems and Mott's argument for "variable-range hopping" Michael Fitzgerald Density functional Theory John Kenison- *
Basic physics of interacting electrons: the Hubbard model, its reduction to the Heisenberg model in the strong-interaction limit, the t-J model; the Mott metal-insulator transition. Pavel Maksimov
Guidelines
- Write-ups should be 4-5 pages in a "Letter style" two-column journal format. The preferred way to do this is to use LaTeX in conjunction with the American Physical Society's RevTeX package. I will post a sample LaTeX file for an article here, closer to the date.
- Write-ups should be serious technical documents: include equations, figures, and references. They should require you to go into the subject in some depth (beyond Wikipedia!)
- Please submit your write-ups in PDF form, with all figures in the main text.
- Presentations will last 8 minutes + 2 minutes for questions/discussion - just a little bit shorter than an APS meeting contributed talk. I will ask you to email me a PDF version of your slides 24 hours before the presentation date, and put them all on one laptop for efficiency.
- Write-ups and talks will be posted on this website unless you have an objection.
- You might find it useful to consult one of the field's master pedagogues, David Mermin, for advice: see What's wrong with these equations? and What's wrong with those talks?