**Office hours**: Tu - 3:00pm-4:00pm

- Electrons in a periodic potential. Bloch theorem. Brillouin zones. Lectures 1 and 2 Addendum on 1D potential and level repulsion,
- Approximations for periodic potential: Weak and strong coupling. Lecture 3 Lecture 4
- Semiclassical dynamics of electrons on a lattice. Bloch oscillations and Wannier-Stark ladder in 1D crystals. Lecture 5
- Semiclassical motion in magnetic field. Bohr-Sommerfeld-Onsager quantization. Lecture 6
- Quantum mechanics of electrons on a lattice. Lecture 7
- (Quantum) Hall effect in band insulators as a consequence of the anomalous velocity in an electric field. Lecture 8
- Quantization of the Hall conductivity in 2D band insulators. Lecture 9
- The Berry phase in quantum mechanics. Lecture 10
- Berry phases for two-level systems. Lecture 11
- Level-degeneracies as monopoles of Berry connection. Lecture 12
- Putting everything together: an explicit two-band model for QHE on a lattice. Normal-topological transitions at band closures. Lecture 13

SUGGESTED READING "Manifestation of Berry's Topological Phase in Neutron Spin Rotation" - do you understand what the last paragraph on page 3 means? In particular, what they mean by "...[Berry phase] can be generated or transformed away by going into a rotating-reference frame..."

- Spin-orbit in atoms and solids. Lecture 14
- Effects of SOI in band structures with and without inversion symmetry. Rashba effect in semiconductor heterostructures. Lecture 15
- Datta-Das transistor. Ballistic Spin Resonance. Spin relaxation in semiconductors. Lecture 16
- Rashba and Dresselhaus SO in GaAs-based 2DEGs. Emergence of the persistent spin helix in semiconductor quantum wells. Optical orientation. Lecture 17
- The Hall effects: Historical overview. The spin current. Lecture 18
- (The lack of) Universal intrinsic SHE in the Rashba 2DEG. Intrinsic SHE in p-doped GaAs. Lecture 19
- Basics of scattering theory. Relation between the scattering amplitude and the T-matrix. Lecture 20
- Skew scattering in 2D. Extrinsic mechanisms in the theory of SHE. Lecture 21 A more complete treatment of skew scattering in 2D (Raikh&Mkhitaryan, PRB 77, 245428 (2008)
- Putting everything together: Phenomenology of coupling between spin and charge currents. The inverse spin Hall effect. Spin injection and spin pumping. Lecture 22
- Basics of kinetics. Lifetime of a particle in a disordered potential. Spin Hall Effect due to skew scattering in 2D. Lecture 23