Effet Hall dans des systèmes quasi-unidimensionnels en interaction

Thierry Giamarchi (Université de Genève) 

Hall effect is one of the most central measures in condensed matter systems. In the most naïve semi-classical theories, it gives access to the number of carriers. We know however that this vision is way too simple and for non-interacting systems the Hall effect has been beautifully connected to the curvature of the Fermi surface and to topological invariants. However, and despite severe efforts, understanding the Hall effect for interacting systems remain an ongoing challenge.

I will show in this talk how one can compute the Hall effect for coupled 1D structures such as ladders, and how using numerical approaches one can predict at large tunnelling between the legs of the latter or large interactions a universal behavior of the Hall coefficient for an interacting ladder.. This prediction will be successfully compared with recent experiments in systems with synthetic gauge fields and synthetic dimensions..

I will also discuss how in the opposite limit of small tunnelling, field theory methods such as bosonisation allow to compute the Hall coefficient and related it to the charge stiffness of the system in the absence of a magnetic field].

Contact : R. Ramazashvili