Topological theory in condensed matter

Diplome(s)

Master ICFP

M2 ICFP

Lieu

Université Paris Cité

Printemps- Eté

Niveau Master 2 3 ECTS - En anglais

Cours en option pour le parcours de Matière Condensée / Physique Quantique M2

Enseignant(s) Christophe MORA ( Université de Paris Cité ) Leonardo MAZZA ( Université Paris-Saclay )

Contact - Secrétariat de l’enseignement

enseignement@phys.ens.fr

The main goal of this course is to provide an introduction to the subject of topological phenomena in condensed-matter.

After an introduction to the mathematical tools, we will focus on electronic models and discuss how topology plays a major role in shaping their physical properties.

We will then move to the quantum Hall effect and discuss its spectacular phenomenology, deeply rooted into topological notions, from robust edge states to fractionalised excitations, such as Majorana fermions.

Syllabus

PART I : Topological theory of free fermions

Introduction : Berry phase, Dirac monopole, Aharanov-Bohm effect, Foucault pendulum
Fermionic models I : SSH model, graphene
Fermionic models II : Haldane model (Chern insulator), Weyl semimetals, topological insulators
Adiabatic pumps à la Thouless
Integer quantum Hall effect

PART II : Topological order and anyons

Topological order and anyons : the toric code
Fractional quantum Hall effect, Laughlin wavefunction
Entanglement in many-body quantum systems

Prerequisites

Evaluation

Written