PHYS-718 / 1 crédit

Enseignant: Holzmann Markus Robert

Langue: Anglais


Frequency

Only this year

Summary

The course will introduce basic concepts for the description of electrons in condensed matter from a microscopic many-body approach, and relate results obtained by quantum field theoretical methods to properties of the many-electron wave functions underlying quantum Monte Carlo calculations.

Content

Description of the behavior of electrons in matter constitutes a big part of condensed matter and solid state theory.
Non-relativistic quantum mechanics, Pauli principle, and Coulomb interaction are enough to formulate a microscopic theory, and ab-initio approaches based on approximate solutions to the many-electron problem have been well established in material science.
However, most of practical descriptions are based on mappings to effectively non-interacting electrons, approximately including Coulomb interactions either phenomenologically (mean-field like) or adding them perturbatively, sometimes both. Despite their enourmous success
in describing and predicting material properties compared to experiment, theoretical justification is less obvious.
In this course, I will briefly introduce numerical and analytical methods which aim to solve the fulll underlying microscopic (electronic) Hamiltonian, or provide a systematic analysis based on quantum field theoretical methods. I will then discuss from a many-body perspective how the common basic description of electrons in matter emerges in terms of non-interacting quasi-particles in normal Fermi liquids or electrons and holes interacting via screened Coulomb interaction in semiconductors.

 


Preliminary outline

  • Numerical approaches: Quantum Monte Carlo methods
  • Analytical methods: Green'€™s functions, perturbation theory, diagrams
  • Many-Fermion wave functions (electron gas)
  • From finite to infinite matter: thermodynamic limit considerations
  • Born-Oppenheimer approximation, nuclear motion, phonons, band-structure
  • Insulator and semiconductors: do electrons interact via bare or screened Coulomb potential?
  • Normal Fermi liquids, Luttinger'€™s theorem
  • ...

Keywords

interacting electrons, Fermi liquid theory, electron gas, diagramatic and quantum Monte Carlo methods

Learning Prerequisites

Recommended courses

quantum mechanics, statistical physics

Learning Outcomes

By the end of the course, the student must be able to:

  • analytical and numerical methods for interacting electrons in normal Fermi liquids (metal) and semiconductors/insulators

Resources

Moodle Link

Dans les plans d'études

  • Forme de l'examen: Oral (session libre)
  • Matière examinée: Condensed matter from a many-electron point of view
  • Cours: 12 Heure(s)
  • Exercices: 2 Heure(s)
  • TP: 2 Heure(s)
  • Type: optionnel

Semaine de référence

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