Topological theory in condensed matter 2022-23

Teachers: Christophe Mora (MPQ, Université de Paris), 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 (although many things have changed!)

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

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

Lecture 6: Topological order and the toric code

Lecture 7: Berry phase and Chern number - recorded video

Lecture 8: Topological order: toric code and anyons

Lecture 9: Topological entanglement entropy