- 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
- Josephson effect, see e.g. Tinkham, Introduction to Superconductivity (2nd edition, paperback, 2004)
- Eliashberg theory, BCS theory as the weak coupling limit of the Eliashberg theory (might be difficult to find literature)
- Superfluidity in cold atomic fermions, BCS-BEC crossover
- Berezinskii–Kosterlitz–Thouless transition
- Superconducting qubits (e.g. basic physics of charge & flux qubits)

- Exact solution for the BCS Hamiltonian (Richardson equations), see e.g. https://arxiv.org/abs/cond-mat/9911058
- Parity effect in superconducting grains, https://arxiv.org/abs/cond-mat/9701041
- Note: last two topics relate to mesoscopic
superconductivity and pairing correlations in nuclei - you can
alternatively choose to present some other topic from this vast field,
e.g. talk about Anderson's theory of dirty superconductors

- Pick a topic from part I, Ch. 3 or from part II of Assa Auerbach, "Interacting Electrons and Quantum Magnetism"
- Pick a topic from John Cardy, "Scaling and Renormalization in Statistical Physics"
- Anderson localization
- Schrieffer–Wolff transformation (see the references therein)

- 1D Ising model in transverse magnetic field (e.g. exact
solution, duality, scaling and RG flow, quantum phase transition,
finite T phase diagram etc.)

- Phase diagram of the 1D XXZ model

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