Week 1: Transport in mesoscopic systems, Historical introduction of Hall effect, Classical Hall effect, Discovery of Quantum Hall Effect (QHE), Two dimensional electron gases (2 DEG), Band diagrams
Week 2: Hall Resistivity and Conductivity, Resistivity measurements, QHE and Metrology, quantization of resistivity, experimental plot of quantized resistivity, Hall and longitudinal resistivity, plateaus, Integer QHE (IQHE)
Week 3: 2DEG in strong magnetic field: Solution of Schroedinger equation, Gauge invariance, Landau gauge, Landau levels degeneracy, quantum of flux, Shubnikov de Haas (SdH) oscillations
Week 4: Laughlin’s argument: Corbino ring, Origin of the plateaux, effect of electric field, inclusion of spins of electrons, Role of disorder, edge states, topological insulator
Week 5: Hall conductivity: Linear response theory, derivation of Kubo formula, choice of gauge potentials, Hall conductivity and Chern number
Week 6: Topological considerations: Gauss-Bonnet theorem, Berry connection and Berry curvature, IQHE revisited in Graphene and 2D Dirac materials, quantization of the plateaus, Graphene nanoribbon.
Week 7: Fractional Quantum Hall effect (FQHE): QHE at non-integer filling fractions, Role of Coulomb interactions, Laughlin wave function, Symmetric gauge, Lowest Landau level, Fractional Statistics, Fractional charge, Anyons, Braiding statistics
Week 8: Spin Hall effect: Spin Orbit coupling, Spin Hall effect, application to spintronics, real materials, HgTe-CdTe quantum wells
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