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
The tutorials are corrected each by a group of two students (possibly three if all slots are taken). Gives additional points to the final exam.
Lectures (in progress)
Lecture 1: Band topology - introduction
Lecture 2: Chern and topological insulator
Lecture 3: Topological superconductors
Lecture 4: (Integer) quantum Hall effect
Lecture 5: Fractional quantum Hall effect (Tuesday, February 13, 2024 - LM)
Lecture 6: Introduction to the toric code (Tuesday, February 13, 2024 - LM)
Lecture 7: Topological order: toric code (Tuesday, February 27, 2024 - LM)
Lecture 8: Topological order: FQHE and anyons (Tuesday, March 5, 2024 - LM)
Lecture 9: Berry phase and Chern number (Tuesday, March 12, 2024 - With Christophe Mora)
Lecture 10: A brief summary on topological order (Tuesday, March 26, 2024 - LM)
Tutorials (in progress)
TD1 The Su-Schrieffer-Heeger (SSH) model (jupyter notebook)
TD2 Bound state at domain wall and protected edge states
TD3 Chern Insulators
TD4 Time-reversal invariant topological insulator
TD5 The Laughlin wavefunction (Tuesday, February 27, 2024 - 9.00AM - LM - solutions)
TD6 The toric code (Tuesday, March 5, 2024 - LM)
TD7 Majorana fermions in Rashba nanowire (Tuesday, March 12, 2024 - With Christophe Mora)
TD8 Anyons in the Laughlin wavefunction (Tuesday, March 19, 2024 - LM)
TD9 Seminar on a recent experimental realisation of the toric code (Tuesday, March 19, 2024 - LM)
TD10 Anyons, topological order and the toric code (Tuesday, March 26, 2024 - LM)
Past examinations
2021-22 EXAM
2022-23 EXAM
Bibliography
Lectures notes by Adolfo 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