Some presentation ideas

  1. Topology in the integer Quantum Hall Effect (Chern numbers, Berry phase, Hofstadter butterfly), see e.g. Y Hatsugai, J. Phys.: Condens. Matter 9 (1997) 2507–2549
  2. Josephson effect, see e.g. Tinkham, Introduction to Superconductivity (2nd edition, paperback, 2004)
  3. Eliashberg theory, BCS theory as the weak coupling limit of the Eliashberg theory (might be difficult to find literature)
  4. Superfluidity in cold atomic fermions, BCS-BEC crossover
  5. Berezinskii–Kosterlitz–Thouless transition
  6. Superconducting qubits (e.g. basic physics of charge & flux qubits)
  7. Exact solution for the BCS Hamiltonian (Richardson equations), see e.g.
  8. Parity effect in superconducting grains,
  9. Pick a topic from part I, Ch. 3 or from part II of Assa Auerbach, "Interacting Electrons and Quantum Magnetism"
  10. Pick a topic from John Cardy, "Scaling and Renormalization in Statistical Physics"
  11. Anderson localization
  12. Schrieffer–Wolff transformation (see the references therein)
  13. 1D Ising model in transverse magnetic field (e.g. exact solution, duality, scaling and RG flow, quantum phase transition, finite T phase diagram etc.)
  14. Phase diagram of the 1D XXZ model

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