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Lecture I : Fermions de Dirac/Weyl en matière condensée : de 1D à 3D - Jérôme Cayssol - Jeudi 4 octobre à 14 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.

In the first lecture (Thursday 4/10/18), I will use the Su-Schrieffer-Heeger and Rice-Mele models to introduce the concepts of Berry-Zak phase, winding numbers and zero energy end states in 1D. Then we will discuss how those ideas can be transposed and extended to 2D lattices, using the Bernevig-Hughes-Zhang model as a typical example of a Chern insulator. The relations between Berry curvature, Chern number, quantized Hall effect will be detailled.