Dirac Matter, topology and interactions in many-particle systems - Département de Physique de l'Ecole Normale supérieure

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Dirac Matter, topology and interactions in many-particle systems

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty : Pascal SIMON
Tutor :
ECTS credits : 3
Language of instruction: Anglais
Site web : https://sites.google.com/site/pascalsimonphysics/

Description

In the past years, condensed matter physics has witnessed tremendous progress with the synthesis of new carbon based materials such as nanotubes and graphene and more recently with the emergence of new exotic materials named topological insulators. The electronic properties of all these materials share the property that they are largely described by solutions of Dirac equations in low dimensions. Simulating Dirac matter in situ with cold atoms in specific optical lattices is also an important direction followed in optics. This course aims at introducing these new emerging concepts to Master 2 students.

Tentative plan of the course

The Dirac equation in low dimensions: generalities.
A closer look at graphene: the massless Dirac equation in two dimensions
Tight-binding model on the honeycomb lattice and the 2D massless Dirac equation
Relativistic Landau levels and quantum Hall effect in grapheme
Introduction to topology in condensed matter physics
Short introduction to topology and differential geometry
Berry phases : generalities
Berry phases in solid states systems
Study of various examples such as the Aharonov-Bohm effect, the semi-classical equation of motion of a Bloch electron, the Berry phase in quantum spin systems
Topologically protected quantities: Chern invariants
Introduction to topological insulators and superconductors
The integer quantum Hall effect and chiral edge states
2D topological insulators and helical edge states
3D topological insulators and topological magnetoelectric effects
Majorana fermions as edge states of topological superconductors

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr