Chapter 1: Superconductivity :
- attractive interaction and Cooper pairing
- BCS theory and excitation spectrum
- order parameter and coherence length
- critical field and vortices
- Cooper pair tunneling in Josephson junctions
Chapter 2: Mesoscopic physics :
- scattering process (electrons, phonons, spin, temperature dependence)
- interference effects (Aharonov-Bohm oscillations, weak localization, spin-orbit interaction)
- ballistic transport (1D conductance, quantum point contacts, quantum Hall effect)
- scattering theory (Landauer-Büttiker formalism, symmetry relations, shot noise)
- quantum dots (level spectrum, Coulomb blockade, stability diagram)
Chapter 3: Topological phases :
- topological invariants, spinors, Berry phase
- 1D SSH model, Kitaev chain, Majorana modes
- 2D systems, Dirac fermions, graphene, Klein tunneling
- quantum Hall effect, Chern numbers, conductance quantization
- topological bands, edge modes, quantum spin Hall
