# Advanced condensed matter: electrons in interaction

## Informations pratiques

Discipline : |
Physique et Chimie |

Niveau : |
Master 2 |

Semestre : |
S3a |

Crédits ECTS : |
6 |

Volume Horaire : |
24h Cours |

Responsable : |

Julia Meyer |

École Normale Supérieure de Lyon, Laboratoire de Physique |

Intervenants : |

## La Formation

In a first course in Condensed Matter, electrons are typically treated as non-interacting particles. In this second course, interaction effects will be studied in detail. We will begin with an introduction to Landau Fermi liquid theory, in which we will develop the idea of quasi-particle excitations and their lifetimes. We will show why, for many systems, the non-interacting Fermi gas is indeed a valid starting point. However, as the interaction strength increases, we will find that different instabilities may occur. We will then turn to low-dimensional systems, where even weak interactions may have a drastic effect. We will show that in a one-dimensional system the elementary excitations are bosonic. Rather than a Fermi liquid, the system is a so-called Tomonaga-Luttinger liquid with power-law decaying correlation functions. Interestingly distinct charge and spin modes appear. Furthermore, we will discuss Coulomb blockade and the Kondo effect in zero-dimensional systems (quantum dots) connected to leads. In particular, we will see that the coupling of a single electron trapped in the quantum dot with the conduction electrons in the leads entails the formation of a strongly correlated many-body state at low temperatures.

## Modalité de l'examen

There will be a written exam at the end of the course. The text will be in English or in French and candidates can write in either language.