ATTENTION SALLE INHABITUELLE: salle de séminaire de l'INSP tour 22-23 salle 317 (3ème étage)
Jérôme Cayssol (LOMA Bordeaux)
Dirac/Weyl fermions in condensed matter: from 1D to 3D
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.
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).