Teachers: Christophe Mora (MPQ, Université Paris Cité), Leonardo Mazza (LPTMS, Université Paris-Saclay)
This course discusses topological phenomena in condensed matter systems. The topics covered in the lectures span from the topology of band structures to the notion of topological order in strongly interacting models. We browse various models with topological features: Chern and topological insulators, topological superconductors with Majorana fermions, the integer and fractional quantum Hall effects, the toric code. We also discuss the spectacular phenomenology resulting from topological properties, from robust edge states to fractionalized excitations, such as Majorana fermions or anyons.
Check out the course of last year
Lectures (in progress)
Lecture 1: Berry phase and Chern number
Lecture 2: Wannier centers and quantum anomalous Hall effect
Lecture 3: Topological band insulators
Lecture 4: Laughlin's flux insertion and Weyl semimetal
Lecture 5: Topological superconductors
Lecture 6: Integer quantum Hall effect
Lecture 7: Fractional quantum Hall effect and Laughlin wavefunction
Lecture 8: Anyons and topological degeneracy
Tutorials (in progress)
TD1 The Su-Schrieffer-Heeger (SSH) model (Jupyter code)
TD2 Chern insulator (Jupyter code)
TD3 Time-reversal invariant topological insulator
TD4 Landau quantization (typos corrected) - Solution
TD5 Forces in the lowest Landau level
TD7 Fractional statistics of Laughlin quasiholes
Previous exams (be careful the program was slightly different). April 2022 - April 2023 - April 2024
Bibliography
Lectures notes by A. Grushin, and the corresponding website
A comprehensive (and inspiring) review on the quantum Hall effect by D. Tong : The quantum Hall effect
A nice review by Asbóth, János et Oroszlány : A Short Course on Topological Insulators
Book by B.A. Bernevig : Topogical insulators and topological superconductors, another one by B. Kotetes : Topological insulators
Lectures notes by David Carpentier
Review article by J.-N. Fuchs and J. Cayssol, Topological and geometrical aspects of band theory
A neat Introduction to the Fractional Quantum Hall Effect by S. Girvin
The unavoidable lectures on Quantum Hall Effects by M. O. Goerbig, great physicist and friend