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Condensed matter: electrons in interaction

Informations pratiques


Discipline :

Physique et Chimie

Niveau :

Master 2

Semestre :

S3a

Crédits ECTS :

6

Volume Horaire :

24h Cours
10h TD

Responsable :

Peter Holdsworth

École Normale Supérieure de Lyon, Laboratoire de Physique

Intervenants :

Peter Holdsworth
Tommaso Roscilde

La Formation

This course will be given in English

In a first course in Condensed Matter, electrons are typically treated as ideal, non-interacting particles in a fixed background potential with crystal symmetry. In this second course the effects of electron interaction with other dynamical degrees of freedom will be studied in detail. We will mainly discuss electron-electron interactions, opening the door for a treatment of interactions with lattice vibrations (phonons) and with magnetic degrees of freedom.

We will begin with an introduction to Landau Fermi liquid theory, in which we will develop the idea of quasi-particle excitations, their lifetimes and the associated quantum coherence length scales. 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 show, at least qualitatively how Fermi liquid theory breaks down allowing the system to undergo a (Mott-Hubbard) metal insulator transition. The metal –insulator transition will be treated through analysis of the Hubbard model, a lattice model, in which the screened Coulomb interaction is approximated by an on-site potential. We will show how an effective coupling develops between translational and spin degrees of freedom through the Pauli exclusion principle, leading to electron-electron repulsion of purely quantum mechanical origin and to the effective Heisenberg spin Hamiltonian in strongly interacting systems. We will show how increasing interaction strength leads to a metal-insulator transition through which electrons become localized around atomic sites. Reference will also be made to “high temperature” superconducting materials, (although no solution will be offered for this open problem). Finally, we will show how the magnetic interaction between conduction electrons and magnetic impurities can lead to trapping of quasi-particles into bound states – the so called Kondo effect. This trapping leads to reduced electron mobility and increased effective mass and hence to “heavy” Fermion quasi-particles.

Pré-requis

Courses from M1 or equivalent: matière condensée, mécanique quantique avancée. The option liquides quantiques M1, is also strongly advised.

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.