Welcome to PHYS 7510, Fall 2013
"The Hall effects: From phenomenology to momentum space topology"
Schedule:Monday -- 2:00pm-3:20pm, Tuesday -- 10:30am-11:50pm.
Instructor: Dima Pesin
Location: JFB 210
Office hours: Tu - 3:00pm-4:00pm
PLAN OF THE COURSE
Homework 1, Due in class on Sep 16th
Solutions for HW1
Homework 2, Due in class on Sep 30th
Solutions for HW2
Homework 3, Due in class on Oct 21th
Solutions for HW3
Homework 4, Due in class on Nov 11th
Solutions for HW4
Part 1: Berry phases and their effect on electronic properties of solids
- 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.
- Semiclassical dynamics of electrons on a lattice. Bloch oscillations and Wannier-Stark ladder in 1D crystals.
- Semiclassical motion in magnetic field. Bohr-Sommerfeld-Onsager quantization.
- Quantum mechanics of electrons on a lattice.
- (Quantum) Hall effect in band insulators as a consequence of the anomalous velocity in an electric field.
- Quantization of the Hall conductivity in 2D band insulators.
- The Berry phase in quantum mechanics.
- Berry phases for two-level systems.
- Level-degeneracies as monopoles of Berry connection.
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..."
- Putting everything together: an explicit two-band model for QHE on a lattice. Normal-topological transitions at band closures.
Part 2: Spin-Orbit interaction effects in solids