final project

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 Hanninen
  • Chern insulators and the quantum anomalous Hall effect (theory + recent experiments) Jen-Ru Chen
  • Kane-Mele model (without Rashba spin-orbit) Alex Stern
  • Landau levels in graphene Mason Eastman
  • Angle-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 Sha
  • Landauer formalism for ballistic conduction (see Datta's book) Claire Gilpin
  • NMR relaxation and Knight shift measurements in solids Kate Rodriguez
  • Quasicrystals, theory and experiment David Mallin
  • *"Heavy fermion" materials
  • Phonons in nanocrystals Sam Keene
  • Basic 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?