You are here

Teaching

Fall 2013, Winter 2016, Winter 2021: PHY 889- Topological condensed matter physics (graduate; see lecture notes below)
Winter 2017-Winter 2020: PHQ 724 - Mesoscopic Physics (graduate)
Summer 2015-2021: PHQ 444 - Statistical Physics II (undergraduate)
Winter 2015-Winter 2021: PHQ 224 - Electricity and Magnetism (undergraduate)

Topological condensed matter physics

Lecture 1: Parallel transport in geometry (I).

Lecture 2: Parallel transport in geometry (II). Parallel transport in quantum mechanics.

Lecture 3: Berry phase and Berry curvature.

Lecture 4: Berry phase of spin in a magnetic field. Chern number. Magnetic monopoles and Dirac strings. Aharonov-Bohm effect.

Lecture 5: Experimental implications of the Berry phase. Non-Abelian Berry phase.

Lecture 6: Berry phase in crystals. Electric polarization of 1D insulators.

Lecture 7: Electric polarization of 1D insulators. Wannier functions. Thouless charge pump (I).

Lecture 8: Thouless charge pump (II). SSH model (I).

Lecture 9: SSH model (III). Topological phase diagram.

Lecture 10: Jackiw-Rebbi zero modes in the SSH model. Kitaev chain (I).

Lecture 11: Topological phase diagram of Kitaev's chain. Majorana zero modes. Experimental realization.

Lecture 12: Topological quantum computation with Majorana zero modes.

Lecture 13: Quantized Hall conductivity in 2D insulators. TKNN formula.

Lecture 14: Quantum Hall insulator. Chiral edge states and quantized Hall conductivity.

Lecture 15: Laughlin's argument. Graphene: low-energy effective Hamiltonian.

Lecture 16: Symmetries of graphene (I): time-reversal.

Lecture 17: Symmetries of graphene (II): space inversion. Gap opening perturbations. Semenoff and Haldane mass.

Lecture 18: Quantum anomalous Hall insulator. Band inversion. Chiral edge states

Lecture 19: Recipe to calculate Chern number for an arbitrary band. Valley Hall effect. Kane-Mele model.

Lecture 20: Quantum spin Hall insulator: helical edge states. Rashba spin-orbit coupling. Z2 invariant (I).

Lecture 21: Recipe to calculate the Z2 invariant for arbitrary bands.

Lecture 22: Simplified formula for Z2 invariant. Introduction to Bernevig-Hughes-Zhang model.

Lecture 23: Topological phase diagram of BHZ model. Experimental discovery.

Lecture 24: Chiral 2D superconductors. Quantized thermal Hall effect. Helical 2D superconductors

Lecture 25: Anomalous velocity and anomalous Hall effect

Lecture 26: Z2 invariants in 3D.

Lecture 27: Strong and weak topological insulators.

Lecture 28: Surface states of 3D topological insulators

Lecture 29: Surface states (conclusion). Bi2Se3: prototype example of 3D topological insulator.

Lecture 30: Low-energy effective model for Bi2Se3. Axion electrodynamics. List of additional topics not covered in class.

Français