Topological theory in condensed matter

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Experimental Internship - Undergraduate program
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November 14 - 18, 2022 :
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Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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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

Responsible : Christophe MORA (MPQ, Université de Paris)

Teachers : Leonardo MAZZA (LPTMS, Université Paris-Saclay), Christophe MORA (MPQ, Université de Paris)

number ECTS : 3

Language of instruction : English

Evaluation : Written

Description :

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.

Plan of the course:

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
Majorana fermions: Kitaev chain and p-wave superfluids
Fractional quantum Hall effect, Laughlin wavefunction and Laughlin pumping
Anyons, the Moore-Read wavefunction and Majorana modes

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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

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