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Lecture II : Fermions de Dirac/Weyl en matière condensée : de 1D à 3D - Jérôme Cayssol - Vendredi 5 octobre à 10 h

INSP - Sorbonne Université - 4 place Jussieu - 75005 Paris - Barre 22-23, 3e étage, salle 317

Jérôme Cayssol - LOMA - Université de Bordeaux

Dirac systems and topological materials are two rapidly growing and evolving fields in modern condensed matter physics, with a very long history from soliton and quantum Hall physics in the early eighties ; and also a more recent history dating from the isolation of graphene in 2004 and the prediction of topological insulators in 2005. In these lectures, i will discuss the topogical aspects of non-interacting fermions on lattices and their relation to Dirac fermions. The goal will be to introduce the basic concepts (topological invariants, quantized electromagnetic response, bulk-boundary correspondance, Dirac fermions, symmetries,…) on simple, yet very rich, models with a progression from one-dimensional (1D) chains to three-dimensional (3D) crystals.

The second lecture (Friday 5/10) will treat further aspects of 2D topological insulators with an emphasis on graphene (Haldane and Kane-Mele models) and a discussion of topological invariants in presence of time-reversal symmetry. I will conclude by a short list of experimental realisations of 1D and 2D topological systems. If time allows, i will discuss briefly 3D topological insulators and semimetals (Dirac and Weyl semimetals).